cairo_draw.py 65.1 KB
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#! /usr/bin/env python
# -*- coding: utf-8 -*-
#
# graph_tool -- a general graph manipulation python module
#
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# Copyright (C) 2006-2015 Tiago de Paula Peixoto <tiago@skewed.de>
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#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

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from __future__ import division, absolute_import, print_function
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import sys
if sys.version_info < (3,):
    range = xrange
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import os
import warnings
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import numpy
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try:
    import cairo
except ImportError:
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    msg = "Error importing cairo. Graph drawing will not work."
    warnings.filterwarnings("always", msg, ImportWarning)
    warnings.warn(msg, ImportWarning)
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    raise
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default_cm = None
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try:
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    import matplotlib.artist
    import matplotlib.backends.backend_cairo
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    import matplotlib.cm
    import matplotlib.colors
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    from matplotlib.cbook import flatten
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    default_clrs = [(0.5529411764705883, 0.8274509803921568, 0.7803921568627451, 1.0),
                    #(1.0, 1.0, 0.7019607843137254, 1.0),
                    (0.7450980392156863, 0.7294117647058823, 0.8549019607843137, 1.0),
                    (0.984313725490196, 0.5019607843137255, 0.4470588235294118, 1.0),
                    (0.5019607843137255, 0.6941176470588235, 0.8274509803921568, 1.0),
                    (0.9921568627450981, 0.7058823529411765, 0.3843137254901961, 1.0),
                    (0.7019607843137254, 0.8705882352941177, 0.4117647058823529, 1.0),
                    (0.9882352941176471, 0.803921568627451, 0.8980392156862745, 1.0),
                    (0.8509803921568627, 0.8509803921568627, 0.8509803921568627, 1.0),
                    (0.7372549019607844, 0.5019607843137255, 0.7411764705882353, 1.0),
                    (0.8, 0.9215686274509803, 0.7725490196078432, 1.0),
                    (1.0, 0.9294117647058824, 0.43529411764705883, 1.0)]
    default_cm = matplotlib.colors.LinearSegmentedColormap.from_list("Set3",
                                                                     default_clrs)
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    is_draw_inline = 'inline' in matplotlib.get_backend()
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except ImportError:
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    msg = "Error importing matplotlib module. Graph drawing will not work."
    warnings.filterwarnings("always", msg, ImportWarning)
    warnings.warn(msg, ImportWarning)
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    raise
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try:
    import IPython.display
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except ImportError:
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    pass

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import numpy as np
import gzip
import bz2
import zipfile
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import copy
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import io
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from collections import defaultdict

from .. import GraphView, PropertyMap, ungroup_vector_property,\
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     group_vector_property, _prop, _check_prop_vector

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from .. stats import label_parallel_edges, label_self_loops

from .. dl_import import dl_import
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dl_import("from . import libgraph_tool_draw")
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try:
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    from .libgraph_tool_draw import vertex_attrs, edge_attrs, vertex_shape,\
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        edge_marker
except ImportError:
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    msg = "Error importing cairo-based drawing library. " + \
        "Was graph-tool compiled with cairomm support?"
    warnings.filterwarnings("always", msg, ImportWarning)
    warnings.warn(msg, ImportWarning)
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from .. draw import sfdp_layout, random_layout, _avg_edge_distance, \
    coarse_graphs

_vdefaults = {
    "shape": "circle",
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    "color": (0.6, 0.6, 0.6, 0.8),
    "fill_color": (0.6470588235294118, 0.058823529411764705, 0.08235294117647059, 0.8),
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    "size": 5,
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    "aspect": 1.,
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    "anchor": 1,
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    "pen_width": 0.8,
    "halo": 0,
    "halo_color": [0., 0., 1., 0.5],
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    "halo_size": 1.5,
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    "text": "",
    "text_color": [0., 0., 0., 1.],
    "text_position": -1.,
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    "text_rotation": 0.,
    "text_offset": [0., 0.],
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    "font_family": "serif",
    "font_slant": cairo.FONT_SLANT_NORMAL,
    "font_weight": cairo.FONT_WEIGHT_NORMAL,
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    "font_size": 12.,
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    "surface": None,
    "pie_fractions": [0.75, 0.25],
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    "pie_colors": default_clrs # ('b', 'g', 'r', 'c', 'm', 'y', 'k')
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    }

_edefaults = {
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    "color": (0.1796875, 0.203125, 0.2109375, 0.8),
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    "pen_width": 1,
    "start_marker": "none",
    "mid_marker": "none",
    "end_marker": "none",
    "marker_size": 4.,
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    "mid_marker_pos": .5,
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    "control_points": [],
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    "gradient": [],
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    "dash_style": [],
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    "text": "",
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    "text_color": (0., 0., 0., 1.),
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    "text_distance": 5,
    "text_parallel": True,
    "font_family": "serif",
    "font_slant": cairo.FONT_SLANT_NORMAL,
    "font_weight": cairo.FONT_WEIGHT_NORMAL,
    "font_size": 12.,
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    "sloppy": False
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    }


def shape_from_prop(shape, enum):
    if isinstance(shape, PropertyMap):
        if shape.key_type() == "v":
            prop = shape.get_graph().new_vertex_property("int")
            descs = shape.get_graph().vertices()
        else:
            descs = shape.get_graph().edges()
            prop = shape.get_graph().new_edge_property("int")
        offset = min(enum.values.keys())
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        vals = dict([(int(k - offset), v) for k, v in enum.values.items()])
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        for v in descs:
            if shape.value_type() == "string":
                prop[v] = int(enum.__dict__[shape[v]])
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            elif int(shape[v]) in vals:
                prop[v] = int(vals[int(shape[v])])
            elif int(shape[v]) - offset in vals:
                prop[v] = int(vals[int(shape[v]) - offset])
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            else:
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                raise ValueError("Invalid value for attribute %s: %s" %
                                 (repr(enum), repr(shape[v])))
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        return prop

    if isinstance(shape, str):
        return int(enum.__dict__[shape])
    else:
        return shape

    raise ValueError("Invalid value for attribute %s: %s" %
                     (repr(enum), repr(shape)))

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def open_file(name, mode="r"):
    name = os.path.expanduser(name)
    base, ext = os.path.splitext(name)
    if ext == ".gz":
        out = gzip.GzipFile(name, mode)
        name = base
    elif ext == ".bz2":
        out = bz2.BZ2File(name, mode)
        name = base
    elif ext == ".zip":
        out = zipfile.ZipFile(name, mode)
        name = base
    else:
        out = open(name, mode)
    fmt = os.path.splitext(name)[1].replace(".", "")
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    return out, fmt
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def get_file_fmt(name):
    name = os.path.expanduser(name)
    base, ext = os.path.splitext(name)
    if ext == ".gz":
        name = base
    elif ext == ".bz2":
        name = base
    elif ext == ".zip":
        name = base
    fmt = os.path.splitext(name)[1].replace(".", "")
    return fmt

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def surface_from_prop(surface):
    if isinstance(surface, PropertyMap):
        if surface.key_type() == "v":
            prop = surface.get_graph().new_vertex_property("object")
            descs = surface.get_graph().vertices()
        else:
            descs = surface.get_graph().edges()
            prop = surface.get_graph().new_edge_property("object")
        surface_map = {}
        for v in descs:
            if surface.value_type() == "string":
                if surface[v] not in surface_map:
                    sfc = gen_surface(surface[v])
                    surface_map[surface[v]] = sfc
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                prop[v] = surface_map[surface[v]]
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            elif surface.value_type() == "python::object":
                if isinstance(surface[v], cairo.Surface):
                    prop[v] = surface[v]
                else:
                    raise ValueError("Invalid value type for surface property: " +
                                     str(type(surface[v])))
            else:
                raise ValueError("Invalid value type for surface property: " +
                                 surface.value_type())
        return prop

    if isinstance(surface, str):
        return gen_surface(surface)
    elif isinstance(surface, cairo.Surface) or surface is None:
        return surface

    raise ValueError("Invalid value for attribute surface: " + repr(surface))

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def centered_rotation(g, pos, text_pos=True):
    x, y = ungroup_vector_property(pos, [0, 1])
    cm = (x.fa.mean(), y.fa.mean())
    dx = x.fa - cm[0]
    dy = y.fa - cm[0]
    angle = g.new_vertex_property("double")
    angle.fa = numpy.arctan2(dy, dx)
    pi = numpy.pi
    angle.fa += 2 * pi
    angle.fa %= 2 * pi
    if text_pos:
        idx = (angle.a > pi / 2 ) * (angle.a < 3 * pi / 2)
        tpos = g.new_vertex_property("double")
        angle.a[idx] += pi
        tpos.a[idx] = pi
        return angle, tpos
    return angle
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def _convert(attr, val, cmap):
    if attr == vertex_attrs.shape:
        return shape_from_prop(val, vertex_shape)
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    if attr == vertex_attrs.surface:
        return surface_from_prop(val)
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    if attr in [edge_attrs.start_marker, edge_attrs.mid_marker,
                edge_attrs.end_marker]:
        return shape_from_prop(val, edge_marker)

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    if attr in [vertex_attrs.pie_colors]:
        if isinstance(val, PropertyMap):
            if val.value_type() in ["vector<double>", "vector<long double>"]:
                return val
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            if val.value_type() in ["vector<int32_t>", "vector<int64_t>", "vector<bool>"]:
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                g = val.get_graph()
                new_val = g.new_vertex_property("vector<double>")
                rg = [float("inf"), -float("inf")]
                for v in g.vertices():
                    for x in val[v]:
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                        rg[0] = min(x, rg[0])
                        rg[1] = max(x, rg[1])
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                if rg[0] == rg[1]:
                    rg[1] = 1
                for v in g.vertices():
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                    new_val[v] = flatten([cmap((x - rg[0]) / (rg[1] - rg[0])) for x in val[v]])
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                return new_val
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            if val.value_type() == "vector<string>":
                g = val.get_graph()
                new_val = g.new_vertex_property("vector<double>")
                for v in g.vertices():
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                    new_val[v] = flatten([matplotlib.colors.ColorConverter().to_rgba(x) for x in val[v]])
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                return new_val
            if val.value_type() == "python::object":
                try:
                    g = val.get_graph()
                    new_val = g.new_vertex_property("vector<double>")
                    for v in g.vertices():
                        try:
                            new_val[v] = [float(x) for x in flatten(val[v])]
                        except ValueError:
                            new_val[v] = flatten([matplotlib.colors.ColorConverter().to_rgba(x) for x in val[v]])
                    return new_val
                except ValueError:
                    pass
        else:
            try:
                return [float(x) for x in flatten(val)]
            except ValueError:
                try:
                    new_val = flatten(matplotlib.colors.ColorConverter().to_rgba(x) for x in val)
                    return list(new_val)
                except ValueError:
                    pass
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    if attr in [vertex_attrs.color, vertex_attrs.fill_color,
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                vertex_attrs.text_color, vertex_attrs.halo_color,
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                edge_attrs.color, edge_attrs.text_color]:
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        if isinstance(val, list):
            return val
        if isinstance(val, (tuple, np.ndarray)):
            return list(val)
        if isinstance(val, str):
            return list(matplotlib.colors.ColorConverter().to_rgba(val))
        if isinstance(val, PropertyMap):
            if val.value_type() in ["vector<double>", "vector<long double>"]:
                return val
            if val.value_type() in ["int32_t", "int64_t", "double",
                                    "long double", "unsigned long", "bool"]:
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                try:
                    vrange = [val.fa.min(), val.fa.max()]
                except ValueError:
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                    vrange = val[val.get_graph().vertex(0)]
                    vrange = [vrange, vrange]
                    for v in val.get_graph().vertices():
                        vrange[0] = min(vrange[0], val[v])
                        vrange[1] = max(vrange[1], val[v])
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                cnorm = matplotlib.colors.Normalize(vmin=vrange[0],
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                                                    vmax=vrange[1])
                if val.key_type() == "v":
                    prop = val.get_graph().new_vertex_property("vector<double>")
                    descs = val.get_graph().vertices()
                else:
                    prop = val.get_graph().new_edge_property("vector<double>")
                    descs = val.get_graph().edges()
                for v in descs:
                    prop[v] = cmap(cnorm(val[v]))
                return prop
            if val.value_type() == "string":
                if val.key_type() == "v":
                    prop = val.get_graph().new_vertex_property("vector<double>")
                    for v in val.get_graph().vertices():
                        prop[v] = matplotlib.colors.ColorConverter().to_rgba(val[v])
                elif val.key_type() == "e":
                    prop = val.get_graph().new_edge_property("vector<double>")
                    for e in val.get_graph().edges():
                        prop[e] = matplotlib.colors.ColorConverter().to_rgba(val[e])
                return prop
        raise ValueError("Invalid value for attribute %s: %s" %
                         (repr(attr), repr(val)))
    return val


def _attrs(attrs, d, g, cmap):
    nattrs = {}
    defaults = {}
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    for k, v in list(attrs.items()):
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        try:
            if d == "v":
                attr = vertex_attrs.__dict__[k]
            else:
                attr = edge_attrs.__dict__[k]
        except KeyError:
            warnings.warn("Unknown attribute: " + k, UserWarning)
            continue
        if isinstance(v, PropertyMap):
            nattrs[int(attr)] = _prop(d, g, _convert(attr, v, cmap))
        else:
            defaults[int(attr)] = _convert(attr, v, cmap)
    return nattrs, defaults


def get_attr(attr, d, attrs, defaults):
    if attr in attrs:
        p = attrs[attr]
    else:
        p = defaults[attr]
    if isinstance(p, PropertyMap):
        return p[d]
    else:
        return p


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def position_parallel_edges(g, pos, loop_angle=float("nan"),
                            parallel_distance=1):
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    lp = label_parallel_edges(GraphView(g, directed=False))
    ll = label_self_loops(g)
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    if isinstance(loop_angle, PropertyMap):
        angle = loop_angle
    else:
        angle = g.new_vertex_property("double")
        angle.a = float(loop_angle)

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    g = GraphView(g, directed=True)
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    if ((len(lp.fa) == 0 or lp.fa.max() == 0) and
        (len(ll.fa) == 0 or ll.fa.max() == 0)):
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        return []
    else:
        spline = g.new_edge_property("vector<double>")
        libgraph_tool_draw.put_parallel_splines(g._Graph__graph,
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                                                _prop("v", g, pos),
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                                                _prop("e", g, lp),
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                                                _prop("e", g, spline),
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                                                _prop("v", g, angle),
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                                                parallel_distance)
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        return spline


def parse_props(prefix, args):
    props = {}
    others = {}
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    for k, v in list(args.items()):
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        if k.startswith(prefix + "_"):
            props[k.replace(prefix + "_", "")] = v
        else:
            others[k] = v
    return props, others


def cairo_draw(g, pos, cr, vprops=None, eprops=None, vorder=None, eorder=None,
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               nodesfirst=False, vcmap=default_cm,
               ecmap=default_cm, loop_angle=float("nan"),
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               parallel_distance=None, fit_view=False, **kwargs):
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    r"""
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    Draw a graph to a :mod:`cairo` context.

    Parameters
    ----------
    g : :class:`~graph_tool.Graph`
        Graph to be drawn.
    pos : :class:`~graph_tool.PropertyMap`
        Vector-valued vertex property map containing the x and y coordinates of
        the vertices.
    cr : :class:`~cairo.Context`
        A :class:`~cairo.Context` instance.
    vprops : dict (optional, default: ``None``)
        Dictionary with the vertex properties. Individual properties may also be
        given via the ``vertex_<prop-name>`` parameters, where ``<prop-name>`` is
        the name of the property.
    eprops : dict (optional, default: ``None``)
        Dictionary with the vertex properties. Individual properties may also be
        given via the ``edge_<prop-name>`` parameters, where ``<prop-name>`` is
        the name of the property.
    vorder : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
        If provided, defines the relative order in which the vertices are drawn.
    eorder : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
        If provided, defines the relative order in which the edges are drawn.
    nodesfirst : bool (optional, default: ``False``)
        If ``True``, the vertices are drawn first, otherwise the edges are.
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    vcmap : :class:`matplotlib.colors.Colormap` (optional, default: :class:`default_cm`)
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        Vertex color map.
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    ecmap : :class:`matplotlib.colors.Colormap` (optional, default: :class:`default_cm`)
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        Edge color map.
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    loop_angle : float or :class:`~graph_tool.PropertyMap` (optional, default: ``nan``)
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        Angle used to draw self-loops. If ``nan`` is given, they will be placed
        radially from the center of the layout.
    parallel_distance : float (optional, default: ``None``)
        Distance used between parallel edges. If not provided, it will be
        determined automatically.
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    fit_view : bool or float (optional, default: ``True``)
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        If ``True``, the layout will be scaled to fit the entire clip region.
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        If a float value is given, it will be interpreted as ``True``, and in
        addition the viewport will be scaled out by that factor.
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    bg_color : str or sequence (optional, default: ``None``)
        Background color. The default is transparent.
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    vertex_* : :class:`~graph_tool.PropertyMap` or arbitrary types (optional, default: ``None``)
        Parameters following the pattern ``vertex_<prop-name>`` specify the
        vertex property with name ``<prop-name>``, as an alternative to the
        ``vprops`` parameter.
    edge_* : :class:`~graph_tool.PropertyMap` or arbitrary types (optional, default: ``None``)
        Parameters following the pattern ``edge_<prop-name>`` specify the edge
        property with name ``<prop-name>``, as an alternative to the ``eprops``
        parameter.
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    """

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    vprops = {} if vprops is None else copy.copy(vprops)
    eprops = {} if eprops is None else copy.copy(eprops)
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    props, kwargs = parse_props("vertex", kwargs)
    vprops.update(props)
    props, kwargs = parse_props("edge", kwargs)
    eprops.update(props)
    for k in kwargs:
        warnings.warn("Unknown parameter: " + k, UserWarning)

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    cr.save()
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    if fit_view != False:
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        extents = cr.clip_extents()
        output_size = (extents[2] - extents[0], extents[3] - extents[1])
        offset, zoom = fit_to_view(g, pos, output_size,
                                   vprops.get("size", _vdefaults["size"]),
                                   vprops.get("pen_width", _vdefaults["pen_width"]),
                                   None, vprops.get("text", None),
                                   vprops.get("font_family",
                                              _vdefaults["font_family"]),
                                   vprops.get("font_size",
                                              _vdefaults["font_size"]),
                                   cr)
        cr.translate(offset[0], offset[1])
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        if not isinstance(fit_view, bool):
            zoom /= fit_view
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        cr.scale(zoom, zoom)

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    if "control_points" not in eprops:
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        if parallel_distance is None:
            parallel_distance = vprops.get("size", _vdefaults["size"])
            if isinstance(parallel_distance, PropertyMap):
                parallel_distance = parallel_distance.fa.mean()
            parallel_distance /= 1.5
            M = cr.get_matrix()
            scale = transform_scale(M, 1,)
            parallel_distance /= scale
        eprops["control_points"] = position_parallel_edges(g, pos, loop_angle,
                                                           parallel_distance)
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    if g.is_directed() and "end_marker" not in eprops:
        eprops["end_marker"] = "arrow"
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    if vprops.get("text_position", None) == "centered":
        angle, tpos = centered_rotation(g, pos, text_pos=True)
        vprops["text_position"] = tpos
        vprops["text_rotation"] = angle

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    vattrs, vdefaults = _attrs(vprops, "v", g, vcmap)
    eattrs, edefaults = _attrs(eprops, "e", g, ecmap)
    vdefs = _attrs(_vdefaults, "v", g, vcmap)[1]
    vdefs.update(vdefaults)
    edefs = _attrs(_edefaults, "e", g, ecmap)[1]
    edefs.update(edefaults)
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    if "control_points" not in eprops:
        if parallel_distance is None:
            parallel_distance = _defaults
        eprops["control_points"] = position_parallel_edges(g, pos, loop_angle,
                                                           parallel_distance)
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    g = GraphView(g, directed=True)
    libgraph_tool_draw.cairo_draw(g._Graph__graph, _prop("v", g, pos),
                                  _prop("v", g, vorder), _prop("e", g, eorder),
                                  nodesfirst, vattrs, eattrs, vdefs, edefs, cr)
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    cr.restore()
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def color_contrast(color):
    c = np.asarray(color)
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    y = c[0] * .299 + c[1] * .587 + c[2] * .114
    if y < .5:
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        c[:3] = 1
    else:
        c[:3] = 0
    return c


def auto_colors(g, bg, pos, back):
    c = g.new_vertex_property("vector<double>")
    for v in g.vertices():
        if isinstance(bg, PropertyMap):
            bgc = bg[v]
        elif isinstance(bg, str):
            bgc = matplotlib.colors.ColorConverter().to_rgba(bg)
        else:
            bgc = bg
        if isinstance(pos, PropertyMap):
            p = pos[v]
        else:
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            if pos == "centered":
                p = 0
            else:
                p = pos
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        if p < 0:
            c[v] = color_contrast(bgc)
        else:
            c[v] = color_contrast(back)
    return c

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def graph_draw(g, pos=None, vprops=None, eprops=None, vorder=None, eorder=None,
               nodesfirst=False, output_size=(600, 600), fit_view=True,
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               inline=is_draw_inline, mplfig=None, output=None, fmt="auto", **kwargs):
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    r"""Draw a graph to screen or to a file using :mod:`cairo`.

    Parameters
    ----------
    g : :class:`~graph_tool.Graph`
        Graph to be drawn.
    pos : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
        Vector-valued vertex property map containing the x and y coordinates of
        the vertices. If not given, it will be computed using :func:`sfdp_layout`.
    vprops : dict (optional, default: ``None``)
        Dictionary with the vertex properties. Individual properties may also be
        given via the ``vertex_<prop-name>`` parameters, where ``<prop-name>`` is
        the name of the property.
    eprops : dict (optional, default: ``None``)
        Dictionary with the vertex properties. Individual properties may also be
        given via the ``edge_<prop-name>`` parameters, where ``<prop-name>`` is
        the name of the property.
    vorder : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
        If provided, defines the relative order in which the vertices are drawn.
    eorder : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
        If provided, defines the relative order in which the edges are drawn.
    nodesfirst : bool (optional, default: ``False``)
        If ``True``, the vertices are drawn first, otherwise the edges are.
    output_size : tuple of scalars (optional, default: ``(600,600)``)
        Size of the drawing canvas. The units will depend on the output format
        (pixels for the screen, points for PDF, etc).
    fit_view : bool (optional, default: ``True``)
        If ``True``, the layout will be scaled to fit the entire display area.
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    inline : bool (optional, default: ``False``)
        If ``True`` and an `IPython notebook <http://ipython.org/notebook>`_  is
        being used, an inline version of the drawing will be returned.
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    mplfig : :mod:`matplotlib` container object (optional, default: ``None``)
        The ``mplfig`` object needs to have an ``artists`` attribute. This can
        for example be a :class:`matplotlib.figure.Figure` or
        :class:`matplotlib.axes.Axes`. Only the cairo backend is supported; use
        ``switch_backend('cairo')``.
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    output : string or file object (optional, default: ``None``)
        Output file name (or object). If not given, the graph will be displayed via
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        :func:`interactive_window`.
    fmt : string (default: ``"auto"``)
        Output file format. Possible values are ``"auto"``, ``"ps"``, ``"pdf"``,
        ``"svg"``, and ``"png"``. If the value is ``"auto"``, the format is
        guessed from the ``output`` parameter.
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    bg_color : str or sequence (optional, default: ``None``)
        Background color. The default is transparent.
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    vertex_* : :class:`~graph_tool.PropertyMap` or arbitrary types (optional, default: ``None``)
        Parameters following the pattern ``vertex_<prop-name>`` specify the
        vertex property with name ``<prop-name>``, as an alternative to the
        ``vprops`` parameter.
    edge_* : :class:`~graph_tool.PropertyMap` or arbitrary types (optional, default: ``None``)
        Parameters following the pattern ``edge_<prop-name>`` specify the edge
        property with name ``<prop-name>``, as an alternative to the ``eprops``
        parameter.
    **kwargs
        Any extra parameters are passed to :func:`~graph_tool.draw.interactive_window`,
        :class:`~graph_tool.draw.GraphWindow`, :class:`~graph_tool.draw.GraphWidget`
        and :func:`~graph_tool.draw.cairo_draw`.

    Returns
    -------
    pos : :class:`~graph_tool.PropertyMap`
        Vector vertex property map with the x and y coordinates of the vertices.
    selected : :class:`~graph_tool.PropertyMap` (optional, only if ``output is None``)
        Boolean-valued vertex property map marking the vertices which were
        selected interactively.

    Notes
    -----


    .. table:: **List of vertex properties**

        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | Name          | Description                                       | Accepted types         | Default Value                    |
        +===============+===================================================+========================+==================================+
        | shape         | The vertex shape. Can be one of the following     | ``str`` or ``int``     | ``"circle"``                     |
        |               | strings: "circle", "triangle", "square",          |                        |                                  |
        |               | "pentagon", "hexagon", "heptagon", "octagon"      |                        |                                  |
        |               | "double_circle", "double_triangle",               |                        |                                  |
        |               | "double_square", "double_pentagon",               |                        |                                  |
        |               | "double_hexagon", "double_heptagon",              |                        |                                  |
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        |               | "double_octagon", "pie".                          |                        |                                  |
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        |               | Optionally, this might take a numeric value       |                        |                                  |
        |               | corresponding to position in the list above.      |                        |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | color         | Color used to stroke the lines of the vertex.     | ``str`` or list of     | ``[0., 0., 0., 1]``              |
        |               |                                                   | ``floats``             |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | fill_color    | Color used to fill the interior of the vertex.    | ``str`` or list of     | ``[0.640625, 0, 0, 0.9]``        |
        |               |                                                   | ``floats``             |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | size          | The size of the vertex, in the default units of   | ``float`` or ``int``   | ``5``                            |
        |               | the output format (normally either pixels or      |                        |                                  |
        |               | points).                                          |                        |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | aspect        | The aspect ratio of the vertex.                   | ``float`` or ``int``   | ``1.0``                          |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | anchor        | Specifies how the edges anchor to the vertices.   |  ``int``               | ``1``                            |
        |               | If `0`, the anchor is at the center of the vertex,|                        |                                  |
        |               | otherwise it is at the border.                    |                        |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | pen_width     | Width of the lines used to draw the vertex, in    | ``float`` or ``int``   | ``0.8``                          |
        |               | the default units of the output format (normally  |                        |                                  |
        |               | either pixels or points).                         |                        |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | halo          | Whether to draw a circular halo around the        | ``bool``               | ``False``                        |
        |               | vertex.                                           |                        |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | halo_color    | Color used to draw the halo.                      | ``str`` or list of     | ``[0., 0., 1., 0.5]``            |
        |               |                                                   | ``floats``             |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | halo_size     | Relative size of the halo.                        | ``float``              | ``1.5``                          |
        |               |                                                   |                        |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | text          | Text to draw together with the vertex.            | ``str``                | ``""``                           |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | text_color    | Color used to draw the text. If the value is      | ``str`` or list of     | ``"auto"``                       |
        |               | ``"auto"``, it will be computed based on          | ``floats``             |                                  |
        |               | fill_color to maximize contrast.                  |                        |                                  |
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        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | text_position | Position of the text relative to the vertex.      | ``float`` or ``int``   | ``-1``                           |
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        |               | If the passed value is positive, it will          |  or ``"centered"``     |                                  |
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        |               | correspond to an angle in radians, which will     |                        |                                  |
        |               | determine where the text will be placed outside   |                        |                                  |
        |               | the vertex. If the value is negative, the text    |                        |                                  |
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        |               | will be placed inside the vertex. If the value is |                        |                                  |
        |               | ``-1``, the vertex size will be automatically     |                        |                                  |
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        |               | increased to accommodate the text. The special    |                        |                                  |
        |               | value ``"centered"`` positions the texts rotated  |                        |                                  |
        |               | radially around the center of mass.               |                        |                                  |
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        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | text_offset   | Text position offset.                             | list of ``float``      | ``[0.0, 0.0]``                   |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | text_rotation | Angle of rotation (in radians) for the text.      | ``float``              | ``0.0``                          |
        |               | The center of rotation is the position of the     |                        |                                  |
        |               | vertex.                                           |                        |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | font_family   | Font family used to draw the text.                | ``str``                | ``"serif"``                      |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | font_slant    | Font slant used to draw the text.                 | ``cairo.FONT_SLANT_*`` | :data:`cairo.FONT_SLANT_NORMAL`  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | font_weight   | Font weight used to draw the text.                | ``cairo.FONT_WEIGHT_*``| :data:`cairo.FONT_WEIGHT_NORMAL` |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | font_size     | Font size used to draw the text.                  | ``float`` or ``int``   | ``12``                           |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | surface       | The cairo surface used to draw the vertex. If     | :class:`cairo.Surface` | ``None``                         |
        |               | the value passed is a string, it is interpreted   | or ``str``             |                                  |
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        |               | as an image file name to be loaded.               |                        |                                  |
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        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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        | pie_fractions | Fractions of the pie sections for the vertices if | list of ``int`` or     | ``[0.75, 0.25]``                 |
        |               | ``shape=="pie"``.                                 | ``float``              |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
        | pie_colors    | Colors used in the pie sections if                | list of strings or     | ``('b','g','r','c','m','y','k')``|
        |               | ``shape=="pie"``.                                 | ``float``.             |                                  |
        +---------------+---------------------------------------------------+------------------------+----------------------------------+
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    .. table:: **List of edge properties**

        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | Name           | Description                                       | Accepted types         | Default Value                    |
        +================+===================================================+========================+==================================+
        | color          | Color used to stroke the edge lines.              | ``str`` or list of     | ``[0.179, 0.203,0.210, 0.8]``    |
        |                |                                                   | floats                 |                                  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | pen_width      | Width of the line used to draw the edge, in       | ``float`` or ``int``   | ``1.0``                          |
        |                | the default units of the output format (normally  |                        |                                  |
        |                | either pixels or points).                         |                        |                                  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
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        | start_marker,  | Edge markers. Can be one of "none", "arrow",      | ``str`` or ``int``     | ``none``                         |
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        | mid_marker,    | "circle", "square", "diamond", or "bar".          |                        |                                  |
        | end_marker     | Optionally, this might take a numeric value       |                        |                                  |
        |                | corresponding to position in the list above.      |                        |                                  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
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        | mid_marker_pos | Relative position of the middle marker.           | ``float``              | ``0.5``                          |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
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        | marker_size    | Size of edge markers, in units appropriate to the | ``float`` or ``int``   | ``4``                            |
        |                | output format (normally either pixels or points). |                        |                                  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | control_points | Control points of a Bézier spline used to draw    | sequence of ``floats`` | ``[]``                           |
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        |                | the edge. Each spline segment requires 6 values   |                        |                                  |
        |                | corresponding to the (x,y) coordinates of the two |                        |                                  |
        |                | intermediary control points and the final point.  |                        |                                  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | gradient       | Stop points of a linear gradient used to stroke   | sequence of ``floats`` | ``[]``                           |
        |                | the edge. Each group of 5 elements is interpreted |                        |                                  |
        |                | as ``[o, r, g, b, a]`` where ``o`` is the offset  |                        |                                  |
        |                | in the range [0, 1] and the remaining values      |                        |                                  |
        |                | specify the colors.                               |                        |                                  |
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        +----------------+---------------------------------------------------+------------------------+----------------------------------+
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        | dash_style     | Dash pattern is specified by an array of positive | sequence of ``floats`` | ``[]``                           |
        |                | values. Each value provides the length of         |                        |                                  |
        |                | alternate "on" and "off" portions of the stroke.  |                        |                                  |
        |                | The last value specifies an offset into the       |                        |                                  |
        |                | pattern at which the stroke begins.               |                        |                                  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
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        | text           | Text to draw next to the edges.                   | ``str``                | ``""``                           |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | text_color     | Color used to draw the text.                      | ``str`` or list of     | ``[0., 0., 0., 1.]``             |
        |                |                                                   | ``floats``             |                                  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | text_distance  | Distance from the edge and its text.              | ``float`` or ``int``   | ``4``                            |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | text_parallel  | If ``True`` the text will be drawn parallel to    | ``bool``               | ``True``                         |
        |                | the edges.                                        |                        |                                  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | font_family    | Font family used to draw the text.                | ``str``                | ``"serif"``                      |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | font_slant     | Font slant used to draw the text.                 | ``cairo.FONT_SLANT_*`` | :data:`cairo.FONT_SLANT_NORMAL`  |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | font_weight    | Font weight used to draw the text.                | ``cairo.FONT_WEIGHT_*``| :data:`cairo.FONT_WEIGHT_NORMAL` |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
        | font_size      | Font size used to draw the text.                  | ``float`` or ``int``   | ``12``                           |
        +----------------+---------------------------------------------------+------------------------+----------------------------------+
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    Examples
    --------
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    .. testcode::
       :hide:

       np.random.seed(42)
       gt.seed_rng(42)
       from numpy import sqrt

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    >>> g = gt.price_network(1500)
    >>> deg = g.degree_property_map("in")
    >>> deg.a = 4 * (sqrt(deg.a) * 0.5 + 0.4)
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    >>> ebet = gt.betweenness(g)[1]
    >>> ebet.a /= ebet.a.max() / 10.
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    >>> eorder = ebet.copy()
    >>> eorder.a *= -1
    >>> pos = gt.sfdp_layout(g)
    >>> control = g.new_edge_property("vector<double>")
    >>> for e in g.edges():
    ...     d = sqrt(sum((pos[e.source()].a - pos[e.target()].a) ** 2)) / 5
    ...     control[e] = [0.3, d, 0.7, d]
    >>> gt.graph_draw(g, pos=pos, vertex_size=deg, vertex_fill_color=deg, vorder=deg,
    ...               edge_color=ebet, eorder=eorder, edge_pen_width=ebet,
    ...               edge_control_points=control, # some curvy edges
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    ...               output="graph-draw.pdf")
    <...>

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    .. testcode::
       :hide:

       gt.graph_draw(g, pos=pos, vertex_size=deg, vertex_fill_color=deg, vorder=deg,
                     edge_color=ebet, eorder=eorder, edge_pen_width=ebet,
                     edge_control_points=control,
                     output="graph-draw.png")


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    .. figure:: graph-draw.*
        :align: center

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        SFDP force-directed layout of a Price network with 1500 nodes. The
        vertex size and color indicate the degree, and the edge color and width
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        the edge betweenness centrality.
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    """

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    vprops = vprops.copy() if vprops is not None else {}
    eprops = eprops.copy() if eprops is not None else {}

    props, kwargs = parse_props("vertex", kwargs)
    vprops.update(props)
    props, kwargs = parse_props("edge", kwargs)
    eprops.update(props)

    if pos is None:
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        if (g.num_vertices() > 2 and output is None and
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            not inline and kwargs.get("update_layout", True)):
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            L = np.sqrt(g.num_vertices())
            pos = random_layout(g, [L, L])
            if g.num_vertices() > 1000:
                if "multilevel" not in kwargs:
                    kwargs["multilevel"] = True
            if "layout_K" not in kwargs:
                kwargs["layout_K"] = _avg_edge_distance(g, pos) / 10
        else:
            pos = sfdp_layout(g)
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    else:
        _check_prop_vector(pos, name="pos", floating=True)
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        if output is None and not inline:
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            if "layout_K" not in kwargs:
                kwargs["layout_K"] = _avg_edge_distance(g, pos)
            if "update_layout" not in kwargs:
                kwargs["update_layout"] = False
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    if "pen_width" in eprops and "marker_size" not in eprops:
        pw = eprops["pen_width"]
        if isinstance(pw, PropertyMap):
            pw = pw.copy()
            pw.a = pw.a * 2.75
            eprops["marker_size"] = pw
        else:
            eprops["marker_size"] = pw * 2.75
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    if "text" in eprops and "text_distance" not in eprops and "pen_width" in eprops:
        pw = eprops["pen_width"]
        if isinstance(pw, PropertyMap):
            pw = pw.copy()
            pw.a *= 2
            eprops["text_distance"] = pw
        else:
            eprops["text_distance"] = pw * 2

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    if "text" in vprops and ("text_color" not in vprops or vprops["text_color"] == "auto"):
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        vcmap = kwargs.get("vcmap", matplotlib.cm.jet)
        bg = _convert(vertex_attrs.fill_color, vprops.get("fill_color", _vdefaults["fill_color"]), vcmap)
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        if "bg_color" in kwargs:
            bg_color = kwargs["bg_color"]
        else:
            bg_color = [1., 1., 1., 1.]
        vprops["text_color"] = auto_colors(g, bg,
                                           vprops.get("text_position",
                                                      _vdefaults["text_position"]),
                                           bg_color)

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    if mplfig:
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        ax = None
        if isinstance(mplfig, matplotlib.figure.Figure):
            ctr = ax = mplfig.gca()
        elif isinstance(mplfig, matplotlib.axes.Axes):
            ctr = ax = mplfig
        else:
            ctr = mplfig

        artist = GraphArtist(g, pos, vprops, eprops, vorder, eorder, nodesfirst,
                             ax, **kwargs)
        ctr.artists.append(artist)

        if fit_view and ax is not None:
            x, y = ungroup_vector_property(pos, [0, 1])
            l, r = x.a.min(), x.a.max()
            b, t = y.a.min(), y.a.max()
            w = r - l
            h = t - b
            ax.set_xlim(l - w * .1, r + w * .1)
            ax.set_ylim(b - h * .1, t + h * .1)

        return pos
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    if inline:
        if fmt == "auto":
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            if output is None:
                fmt = "png"
            else:
                fmt = get_file_fmt(output)
        output_file = output
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        output = io.BytesIO()

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    if output is None:
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        for p, val in vprops.items():
            if isinstance(val, PropertyMap):
                vprops[p] = _convert(vertex_attrs.__dict__[p], val,
                                     kwargs.get("vcmap", default_cm))
        for p, val in eprops.items():
            if isinstance(val, PropertyMap):
                eprops[p] = _convert(edge_attrs.__dict__[p], val,
                                     kwargs.get("ecmap", default_cm))
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        return interactive_window(g, pos, vprops, eprops, vorder, eorder,
                                  nodesfirst, **kwargs)
    else:
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        if isinstance(output, str):
            out, auto_fmt = open_file(output, mode="wb")
        else:
            out = output
            if fmt == "auto":
                raise ValueError("File format must be specified.")
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        if fmt == "auto":
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            fmt = auto_fmt
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        if fmt == "pdf":
            srf = cairo.PDFSurface(out, output_size[0], output_size[1])
        elif fmt == "ps":
            srf = cairo.PSSurface(out, output_size[0], output_size[1])
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        elif fmt == "eps":
            srf = cairo.PSSurface(out, output_size[0], output_size[1])
            srf.set_eps(True)
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        elif fmt == "svg":
            srf = cairo.SVGSurface(out, output_size[0], output_size[1])
        elif fmt == "png":
            srf = cairo.ImageSurface(cairo.FORMAT_ARGB32, output_size[0],
                                     output_size[1])
        else:
            raise ValueError("Invalid format type: " + fmt)

        cr = cairo.Context(srf)

        adjust_default_sizes(g, output_size, vprops, eprops)
        if fit_view:
            offset, zoom = fit_to_view(g, pos, output_size, vprops["size"],
                                       vprops["pen_width"], None,
                                       vprops.get("text", None),
                                       vprops.get("font_family",
                                                  _vdefaults["font_family"]),
                                       vprops.get("font_size",
                                                  _vdefaults["font_size"]),
                                       cr)
        else:
            offset, zoom = [0, 0], 1

        if "bg_color" in kwargs:
            bg_color = kwargs["bg_color"]
            del  kwargs["bg_color"]
            cr.set_source_rgba(bg_color[0], bg_color[1],
                               bg_color[2], bg_color[3])
            cr.paint()
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        cr.translate(offset[0], offset[1])
        cr.scale(zoom, zoom)

        cairo_draw(g, pos, cr, vprops, eprops, vorder, eorder,
                   nodesfirst, **kwargs)
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        if fmt == "png":
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            srf.write_to_png(out)
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        del cr

        if inline:
            img = None
            if fmt == "png":
                img = IPython.display.Image(data=out.getvalue())
            if fmt == "svg":
                img = IPython.display.SVG(data=out.getvalue())
            if img is None:
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                inl_out = io.BytesIO()
                inl_srf = cairo.ImageSurface(cairo.FORMAT_ARGB32,
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                                             output_size[0],
                                             output_size[1])
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                inl_cr = cairo.Context(inl_srf)
                inl_cr.set_source_surface(srf, 0, 0)
                inl_cr.paint()
                inl_srf.write_to_png(inl_out)
                del inl_srf
                img = IPython.display.Image(data=inl_out.getvalue())
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            srf.finish()
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            if output_file is not None:
                if isinstance(output_file, str):
                    ofile, auto_fmt = open_file(output_file, mode="wb")
                else:
                    ofile = output_file
                ofile.write(out.getvalue())
                if isinstance(output_file, str):
                    ofile.close()
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            IPython.display.display(img)
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        del srf
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        return pos
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def adjust_default_sizes(g, geometry, vprops, eprops, force=False):
    if "size" not in vprops or force:
        A = geometry[0] * geometry[1]
        vprops["size"] = np.sqrt(A / g.num_vertices()) / 3.5

    if "pen_width" not in vprops or force:
        size = vprops["size"]
        if isinstance(vprops["size"], PropertyMap):
            size = vprops["size"].fa.mean()
        vprops["pen_width"] = size / 10
        if "pen_width" not in eprops or force:
            eprops["pen_width"] = size / 10
        if "marker_size" not in eprops or force:
            eprops["marker_size"] = size * 0.8


def scale_ink(scale, vprops, eprops):
    if "size" not in vprops:
        vprops["size"] = _vdefaults["size"]
    if "pen_width" not in vprops:
        vprops["pen_width"] = _vdefaults["pen_width"]
    if "font_size" not in vprops:
        vprops["font_size"] = _vdefaults["font_size"]
    if "pen_width" not in eprops:
        eprops["pen_width"] = _edefaults["pen_width"]
    if "marker_size" not in eprops:
        eprops["marker_size"] = _edefaults["marker_size"]
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    if "font_size" not in eprops:
        eprops["font_size"] = _edefaults["font_size"]
    if "text_distance" not in eprops:
        eprops["text_distance"] = _edefaults["text_distance"]
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    for props in [vprops, eprops]:
        if isinstance(props["pen_width"], PropertyMap):
            props["pen_width"].fa *= scale
        else:
            props["pen_width"] *= scale
    if isinstance(vprops["size"], PropertyMap):
        vprops["size"].fa *= scale
    else:
        vprops["size"] *= scale
    if isinstance(vprops["font_size"], PropertyMap):
        vprops["font_size"].fa *= scale
    else:
        vprops["font_size"] *= scale
    if isinstance(eprops["marker_size"], PropertyMap):
        eprops["marker_size"].fa *= scale
    else:
        eprops["marker_size"] *= scale
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    if isinstance(eprops["font_size"], PropertyMap):
        eprops["font_size"].fa *= scale
    else:
        eprops["font_size"] *= scale
    if isinstance(eprops["text_distance"], PropertyMap):
        eprops["text_distance"].fa *= scale
    else:
        eprops["text_distance"] *= scale
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def get_bb(g, pos, size, pen_width, size_scale=1, text=None, font_family=None,
           font_size=None, cr=None):
    size = size.fa[:g.num_vertices()] if isinstance(size, PropertyMap) else size
    pen_width = pen_width.fa if isinstance(pen_width, PropertyMap) else pen_width
    pos_x, pos_y = ungroup_vector_property(pos, [0, 1])
    if text is not None and text != "":
        if not isinstance(size, PropertyMap):
            uniform = (not isinstance(font_size, PropertyMap) and
                       not isinstance(font_family, PropertyMap))
            size = np.ones(len(pos_x.fa)) * size
        else:
            uniform = False
        for i, v in enumerate(g.vertices()):
            ff = font_family[v] if isinstance(font_family, PropertyMap) \
               else font_family
            cr.select_font_face(ff)
            fs = font_size[v] if isinstance(font_family, PropertyMap) \
               else font_size
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            if not isinstance(font_size, PropertyMap):
                cr.set_font_size(fs)
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            t = text[v] if isinstance(text, PropertyMap) else text
            if not isinstance(t, str):
                t = str(t)
            extents = cr.text_extents(t)
            s = max(extents[2], extents[3]) * 1.4
            size[i] = max(size[i] * size_scale, s) / size_scale
            if uniform:
                size[:] = size[i]
                break
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    sl = label_self_loops(g)
    slm = sl.a.max() * 0.75
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    delta = (size * size_scale * (slm + 1)) / 2 + pen_width * 2
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    x_range = [pos_x.fa.min(), pos_x.fa.max()]
    y_range = [pos_y.fa.min(), pos_y.fa.max()]
    x_delta = [x_range[0] - (pos_x.fa - delta).min(),
               (pos_x.fa + delta).max() - x_range[1]]
    y_delta = [y_range[0] - (pos_y.fa - delta).min(),
               (pos_y.fa + delta).max() - y_range[1]]
    return x_range, y_range, x_delta, y_delta


def fit_to_view(g, pos, geometry, size, pen_width, M=None, text=None,
                font_family=None, font_size=None, cr=None):
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    if g.num_vertices() == 0:
        return [0, 0], 1
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    if M is not None:
        pos_x, pos_y = ungroup_vector_property(pos, [0, 1])
        P = np.zeros((2, len(pos_x.fa)))
        P[0, :] = pos_x.fa
        P[1, :] = pos_y.fa
        T = np.zeros((2, 2))
        O = np.zeros(2)
        T[0, 0], T[1, 0], T[0, 1], T[1, 1], O[0], O[1] = M
        P = np.dot(T, P)
        P[0] += O[0]
        P[1] += O[1]
        pos_x.fa = P[0, :]
        pos_y.fa = P[1, :]
        pos = group_vector_property([pos_x, pos_y])
    x_range, y_range, x_delta, y_delta = get_bb(g, pos, size, pen_width,
                                                1, text, font_family,
                                                font_size, cr)
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    dx = (x_range[1] - x_range[0])
    dy = (y_range[1] - y_range[0])
    if dx == 0:
        dx = 1
    if dy == 0:
        dy = 1
    zoom_x = (geometry[0] - sum(x_delta)) / dx
    zoom_y = (geometry[1] - sum(y_delta)) / dy
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    if np.isnan(zoom_x) or np.isinf(zoom_x) or zoom_x == 0:
        zoom_x = 1
    if np.isnan(zoom_y) or np.isinf(zoom_y) or zoom_y == 0:
        zoom_y = 1
    pad = 0.95
    zoom = min(zoom_x, zoom_y) * pad
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    empty_x = (geometry[0] - sum(x_delta)) - dx * zoom
    empty_y = (geometry[1] - sum(y_delta)) - dy * zoom
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    offset = [-x_range[0] * zoom + empty_x / 2 + x_delta[0],
              -y_range[0] * zoom + empty_y / 2 + y_delta[0]]
    return offset, zoom


def transform_scale(M, scale):
    p = M.transform_distance(scale / np.sqrt(2),
                             scale / np.sqrt(2))
    return np.sqrt(p[0] ** 2 + p[1] ** 2)

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def get_hierarchy_control_points(g, t, tpos, beta=0.8, cts=None):
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    r"""Return the Bézier spline control points for the edges in ``g``, given the hierarchical structure encoded in graph `t`.
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    Parameters
    ----------
    g : :class:`~graph_tool.Graph`
        Graph to be drawn.
    t : :class:`~graph_tool.Graph`
        Directed graph containing the hierarchy of ``g``. It must be a directed
        tree with a single root. The direction of the edges point from the root
        to the leaves, and the vertices in ``t`` with index in the range
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        :math:`[0, N-1]`, with :math:`N` being the number of vertices in ``g``,
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        must correspond to the respective vertex in ``g``.
    tpos : :class:`~graph_tool.PropertyMap`
        Vector-valued vertex property map containing the x and y coordinates of
        the vertices in graph ``t``.
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    beta : ``float`` (optional, default: ``0.8`` or :class:`~graph_tool.PropertyMap`)
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        Edge bundling strength. For ``beta == 0`` the edges are straight lines,
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        and for ``beta == 1`` they strictly follow the hierarchy. This can be
        optionally an edge property map, which specified a different bundling
        strength for each edge.
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    cts : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
        Edge property map of type ``vector<double>`` where the control points
        will be stored.

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    Returns
    -------

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    cts : :class:`~graph_tool.PropertyMap`
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        Vector-valued edge property map containing the Bézier spline control
        points for the edges in ``g``.

    Notes
    -----
    This is an implementation of the edge-bundling algorithm described in
    [holten-hierarchical-2006]_.


    Examples
    --------
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    .. testsetup:: nested_cts

       gt.seed_rng(42)
       np.random.seed(42)

    .. doctest:: nested_cts

       >>> g = gt.collection.data["netscience"]
       >>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))
       >>> g.purge_vertices()
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       >>> state = gt.minimize_nested_blockmodel_dl(g, deg_corr=True)
       >>> bstack = state.get_bstack()
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       >>> t = gt.get_hierarchy_tree(bstack)[0]
       >>> tpos = pos = gt.radial_tree_layout(t, t.vertex(t.num_vertices() - 1), weighted=True)
       >>> cts = gt.get_hierarchy_control_points(g, t, tpos)
       >>> pos = g.own_property(tpos)
       >>> b = bstack[0].vp["b"]
       >>> gt.graph_draw(g, pos=pos, vertex_fill_color=b, vertex_shape=b, edge_control_points=cts,
       ...               edge_color=[0, 0, 0, 0.3], vertex_anchor=0, output="netscience_nested_mdl.pdf")
       <...>

    .. testcleanup:: nested_cts

       gt.graph_draw(g, pos=pos, vertex_fill_color=b, vertex_shape=b, edge_control_points=cts, edge_color=[0, 0, 0, 0.3], vertex_anchor=0, output="netscience_nested_mdl.png")

    .. figure:: netscience_nested_mdl.*
       :align: center

       Block partition of a co-authorship network, which minimizes the description
       length of the network according to the nested (degree-corrected) stochastic blockmodel.

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    References
    ----------

    .. [holten-hierarchical-2006] Holten, D. "Hierarchical Edge Bundles:
       Visualization of Adjacency Relations in Hierarchical Data.", IEEE
       Transactions on Visualization and Computer Graphics 12, no. 5, 741–748
       (2006). :doi:`10.1109/TVCG.2006.147`
    """

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    if cts is None:
        cts = g.new_edge_property("vector<double>")
    if cts.value_type() != "vector<double>":
        raise ValueError("cts property map must be of type 'vector<double>' not '%s' " % cts.value_type())
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    u = GraphView(g, directed=True)
    tu = GraphView(t, directed=True)

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    if not isinstance(beta, PropertyMap):
        beta = u.new_edge_property("double", beta)
    else:
        beta = beta.copy("double")

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    libgraph_tool_draw.get_cts(u._Graph__graph, tu._Graph__graph,
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                               _prop("v", tu, tpos),
                               _prop("e", u, beta),
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                               _prop("e", u, cts))
    return cts
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#
# The functions and classes below depend on GTK
# =============================================
#

try:
    from gi.repository import Gtk, Gdk, GdkPixbuf
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    from gi.repository import GObject as gobject
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    from .gtk_draw import *
except (ImportError, RuntimeError) as e:
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    msg = "Error importing Gtk module: %s; GTK+ drawing will not work." % str(e)
    warnings.filterwarnings("always", msg, ImportWarning)
    warnings.warn(msg, ImportWarning)
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def gen_surface(name):
    fobj, fmt = open_file(name)
    if fmt in ["png", "PNG"]:
        sfc = cairo.ImageSurface.create_from_png(fobj)
        return sfc
    else:
        pixbuf = GdkPixbuf.Pixbuf.new_from_file(name)
        surface = cairo.ImageSurface(cairo.FORMAT_ARGB32, pixbuf.get_width(),
                                     pixbuf.get_height())
        cr = cairo.Context(surface)
        Gdk.cairo_set_source_pixbuf(cr, pixbuf, 0, 0)
        cr.paint()
        return surface
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# matplotlib
# ==========

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class GraphArtist(matplotlib.artist.Artist):
    """:class:`matplotlib.artist.Artist` specialization that draws
       :class:`graph_tool.Graph` instances.

    .. warning::

        Only Cairo-based backends are supported.
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    """

    def __init__(self, g, pos, vprops, eprops, vorder, eorder,
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                nodesfirst, ax=None, **kwargs):
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        matplotlib.artist.Artist.__init__(self)
        self.g = g
        self.pos = pos
        self.vprops = vprops
        self.eprops = eprops
        self.vorder = vorder
        self.eorder = eorder
        self.nodesfirst = nodesfirst
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        self.ax = ax
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        self.kwargs = kwargs

    def draw(self, renderer):
        if not isinstance(renderer, matplotlib.backends.backend_cairo.RendererCairo):
            raise NotImplementedError("graph plotting is supported only on Cairo backends")
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        ctx = renderer.gc.ctx
        ctx.save()

        if self.ax is not None:
            m = self.ax.transData.get_affine().get_matrix()
            m = cairo.Matrix(m[0,0], m[1, 0], m[0, 1], m[1, 1], m[0, 2], m[1,2])
            ctx.set_matrix(m)

            l, r = self.ax.get_xlim()
            b, t = self.ax.get_ylim()
            ctx.rectangle(l, b, r-l, t-b)
            ctx.clip()


        cairo_draw(self.g, self.pos, ctx, self.vprops, self.eprops,
                   self.vorder, self.eorder, self.nodesfirst, self.kwargs)

        ctx.restore()