__init__.py 82 KB
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#! /usr/bin/env python
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# -*- coding: utf-8 -*-
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#
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# graph_tool -- a general graph manipulation python module
#
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# Copyright (C) 2006-2013 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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"""
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graph_tool - efficient graph analysis and manipulation
======================================================

Summary
-------

.. autosummary::
   :nosignatures:

   Graph
   GraphView
   Vertex
   Edge
   PropertyMap
   PropertyArray
   load_graph
   group_vector_property
   ungroup_vector_property
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   infect_vertex_property
   edge_difference
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   value_types
   show_config

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This module provides:
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   1. A :class:`~graph_tool.Graph` class for graph representation and manipulation
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   2. Property maps for Vertex, Edge or Graph.
   3. Fast algorithms implemented in C++.
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How to use the documentation
----------------------------
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Documentation is available in two forms: docstrings provided
with the code, and the full documentation available in
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`the graph-tool homepage <http://graph-tool.skewed.de>`_.
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We recommend exploring the docstrings using `IPython
<http://ipython.scipy.org>`_, an advanced Python shell with TAB-completion and
introspection capabilities.

The docstring examples assume that ``graph_tool.all`` has been imported as
``gt``::

   >>> import graph_tool.all as gt

Code snippets are indicated by three greater-than signs::

   >>> x = x + 1

Use the built-in ``help`` function to view a function's docstring::

   >>> help(gt.Graph)

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Contents
--------
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"""
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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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__author__ = "Tiago de Paula Peixoto <tiago@skewed.de>"
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__copyright__ = "Copyright 2006-2013 Tiago de Paula Peixoto"
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__license__ = "GPL version 3 or above"
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__URL__ = "http://graph-tool.skewed.de"
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# import numpy and scipy before everything to avoid weird segmentation faults
# depending on the order things are imported.

import numpy
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import numpy.ma
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import scipy
import scipy.stats

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from .dl_import import *
dl_import("from . import libgraph_tool_core as libcore")
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__version__ = libcore.mod_info().version

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from . import io  # sets up libcore io routines
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import sys
import os
import re
import gzip
import weakref
import copy

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from io import BytesIO
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from .decorators import _wraps, _require, _attrs, _limit_args
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from inspect import ismethod
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__all__ = ["Graph", "GraphView", "Vertex", "Edge", "Vector_bool",
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           "Vector_int16_t", "Vector_int32_t", "Vector_int64_t", "Vector_double",
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           "Vector_long_double", "Vector_string", "value_types", "load_graph",
           "PropertyMap", "group_vector_property", "ungroup_vector_property",
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           "infect_vertex_property", "edge_difference", "seed_rng", "show_config",
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           "PropertyArray", "__author__", "__copyright__", "__URL__",
           "__version__"]
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# this is rather pointless, but it works around a sphinx bug
graph_tool = sys.modules[__name__]
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################################################################################
# Utility functions
################################################################################


def _prop(t, g, prop):
    """Return either a property map, or an internal property map with a given
    name."""
    if type(prop) == str:
        try:
            pmap = g.properties[(t, prop)]
        except KeyError:
            raise KeyError("no internal %s property named: %s" %\
                           ("vertex" if t == "v" else \
                            ("edge" if t == "e" else "graph"), prop))
    else:
        pmap = prop
    if pmap == None:
        return libcore.any()
    else:
        if t != prop.key_type():
            names = {'e': 'edge', 'v': 'vertex', 'g': 'graph'}
            raise ValueError("Expected '%s' property map, got '%s'" %
                             (names[t], names[prop.key_type()]))
        return pmap._PropertyMap__map.get_map()


def _degree(g, name):
    """Retrieve the degree type from string, or returns the corresponding
    property map."""
    deg = name
    if name == "in-degree" or name == "in":
        deg = libcore.Degree.In
    elif name == "out-degree" or name == "out":
        deg = libcore.Degree.Out
    elif name == "total-degree" or name == "total":
        deg = libcore.Degree.Total
    else:
        deg = _prop("v", g, deg)
    return deg


def _type_alias(type_name):
    alias = {"int8_t": "bool",
             "boolean": "bool",
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             "short": "int16_t",
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             "int": "int32_t",
             "long": "int64_t",
             "long long": "int64_t",
             "object": "python::object",
             "float": "double"}
    if type_name in value_types():
        return type_name
    if type_name in alias:
        return alias[type_name]
    ma = re.compile(r"vector<(.*)>").match(type_name)
    if ma:
        t = ma.group(1)
        if t in alias:
            return "vector<%s>" % alias[t]
    raise ValueError("invalid property value type: " + type_name)


def _python_type(type_name):
    type_name = _type_alias(type_name)
    if "vector" in type_name:
        ma = re.compile(r"vector<(.*)>").match(type_name)
        t = ma.group(1)
        return list, _python_type(t)
    if "int" in type_name:
        return int
    if type_name == "bool":
        return bool
    if "double" in type_name:
        return float
    if "string" in type_name:
        return str
    return object


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def _gt_type(obj):
    t = type(obj)
    if t is numpy.longlong or t is numpy.uint64:
        return "long long"
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    if issubclass(t, numpy.int16):
        return "short"
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    if t is int or issubclass(t, numpy.int):
        return "int"
    if t is numpy.float128:
        return "long double"
    if t is float or issubclass(t, numpy.float):
        return "double"
    if t is str:
        return "string"
    if t is bool:
        return "bool"
    if issubclass(t, list) or issubclass(t, numpy.ndarray):
        return "vector<%s>" % _gt_type(obj[0])
    return "object"


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def _convert(prop, val):
    # attempt to convert to a compatible python type. This is useful,
    # for instance, when dealing with numpy types.
    vtype = _python_type(prop.value_type())
    if type(vtype) is tuple:
        return [vtype[1](x) for x in val]
    return vtype(val)


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def show_config():
    """Show ``graph_tool`` build configuration."""
    info = libcore.mod_info()
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    print("version:", info.version)
    print("gcc version:", info.gcc_version)
    print("compilation flags:", info.cxxflags)
    print("install prefix:", info.install_prefix)
    print("python dir:", info.python_dir)
    print("graph filtering:", libcore.graph_filtering_enabled())
    print("openmp:", libcore.openmp_enabled())
    print("uname:", " ".join(os.uname()))
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################################################################################
# Property Maps
################################################################################


class PropertyArray(numpy.ndarray):
    """This is a :class:`~numpy.ndarray` subclass which keeps a reference of its :class:`~graph_tool.PropertyMap` owner, and detects if the underlying data has been invalidated."""

    __array_priority__ = -10

    def _get_pmap(self):
        return self._prop_map

    def _set_pmap(self, value):
        self._prop_map = value

    prop_map = property(_get_pmap, _set_pmap,
                        doc=":class:`~graph_tool.PropertyMap` owner instance.")

    def __new__(cls, input_array, prop_map):
        obj = numpy.asarray(input_array).view(cls)
        obj.prop_map = prop_map

        # check if data really belongs to property map
        if (prop_map._get_data().__array_interface__['data'][0] !=
            obj._get_base_data()):
            obj.prop_map = None
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            # do a copy
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            obj = numpy.asarray(obj)

        return obj

    def _get_base(self):
        base = self
        while base.base is not None:
            base = base.base
        return base

    def _get_base_data(self):
        return self._get_base().__array_interface__['data'][0]

    def _check_data(self):
        if self.prop_map is None:
            return

        data = self.prop_map._get_data()

        if (data is None or
            data.__array_interface__['data'][0] != self._get_base_data()):
            raise ValueError(("The graph correspondig to the underlying" +
                              " property map %s has changed. The" +
                              " PropertyArray at 0x%x is no longer valid!") %
                             (repr(self.prop_map), id(self)))

    def __array_finalize__(self, obj):
        if type(obj) is PropertyArray:
            obj._check_data()

        if obj is not None:
            # inherit prop_map only if the data is the same
            if (type(obj) is PropertyArray and
                self._get_base_data() == obj._get_base_data()):
                self.prop_map = getattr(obj, 'prop_map', None)
            else:
                self.prop_map = None
        self._check_data()

    def __array_prepare__(self, out_arr, context=None):
        self._check_data()
        return numpy.ndarray.__array_prepare__(self, out_arr, context)

    def __array_wrap__(self, out_arr, context=None):
        #demote to ndarray
        obj = numpy.ndarray.__array_wrap__(self, out_arr, context)
        return numpy.asarray(obj)

    # Overload members and operators to add data checking

    def _wrap_method(method):
        method = getattr(numpy.ndarray, method)

        def checked_method(self, *args, **kwargs):
            self._check_data()
            return method(self, *args, **kwargs)

        if ismethod(method):
            checked_method = _wraps(method)(checked_method)
        checked_method.__doc__ = getattr(method, "__doc__", None)
        return checked_method

    for method in ['all', 'any', 'argmax', 'argmin', 'argsort', 'astype',
                   'byteswap', 'choose', 'clip', 'compress', 'conj',
                   'conjugate', 'copy', 'cumprod', 'cumsum', 'diagonal', 'dot',
                   'dump', 'dumps', 'fill', 'flat', 'flatten', 'getfield',
                   'imag', 'item', 'itemset', 'itemsize', 'max', 'mean', 'min',
                   'newbyteorder', 'nonzero', 'prod', 'ptp', 'put', 'ravel',
                   'real', 'repeat', 'reshape', 'resize', 'round',
                   'searchsorted', 'setfield', 'setflags', 'sort', 'squeeze',
                   'std', 'sum', 'swapaxes', 'take', 'tofile', 'tolist',
                   'tostring', 'trace', 'transpose', 'var', 'view',
                   '__getitem__']:
        if hasattr(numpy.ndarray, method):
            locals()[method] = _wrap_method(method)


class PropertyMap(object):
    """This class provides a mapping from vertices, edges or whole graphs to arbitrary properties.

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    See :ref:`sec_property_maps` for more details.

    The possible property value types are listed below.
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    .. table::

        =======================     ======================
         Type name                  Alias
        =======================     ======================
        ``bool``                    ``uint8_t``
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        ``int16_t``                 ``short``
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        ``int32_t``                 ``int``
        ``int64_t``                 ``long``, ``long long``
        ``double``                  ``float``
        ``long double``
        ``string``
        ``vector<bool>``            ``vector<uint8_t>``
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        ``vector<int16_t>``         ``short``
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        ``vector<int32_t>``         ``vector<int>``
        ``vector<int64_t>``         ``vector<long>``, ``vector<long long>``
        ``vector<double>``          ``vector<float>``
        ``vector<long double>``
        ``vector<string>``
        ``python::object``          ``object``
        =======================     ======================
    """
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    def __init__(self, pmap, g, key_type):
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        self.__map = pmap
        self.__g = weakref.ref(g)
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        self.__base_g = lambda: None
        try:
            if isinstance(g, GraphView):
                self.__base_g = weakref.ref(g.base)  # keep reference to the
                                                     # base graph, in case the
                                                     # graph view is deleted.
        except NameError:
            pass  # ignore if GraphView is yet undefined
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        self.__key_type = key_type
        self.__register_map()

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    def __key_trans(self, key):
        if self.key_type() == "g":
            return key._Graph__graph
        else:
            return key


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    def __register_map(self):
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        for g in [self.__g(), self.__base_g()]:
            if g is not None:
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                g._Graph__known_properties[id(self)] = weakref.ref(self)
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    def __unregister_map(self):
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        for g in [self.__g(), self.__base_g()]:
            if g is not None:
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                del g._Graph__known_properties[id(self)]
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    def __del__(self):
        self.__unregister_map()

    def __getitem__(self, k):
        return self.__map[self.__key_trans(k)]

    def __setitem__(self, k, v):
        key = self.__key_trans(k)
        try:
            self.__map[key] = v
        except TypeError:
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            self.__map[key] = _convert(self, v)
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    def __repr__(self):
        # provide some more useful information
        if self.key_type() == "e":
            k = "Edge"
        elif self.key_type() == "v":
            k = "Vertex"
        else:
            k = "Graph"
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        g = self.get_graph()
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        if g == None:
            g = "a non-existent graph"
        else:
            g = "Graph 0x%x" % id(g)
        return ("<PropertyMap object with key type '%s' and value type '%s',"
                + " for %s, at 0x%x>") % (k, self.value_type(), g, id(self))

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    def copy(self, value_type=None):
        """Return a copy of the property map. If ``value_type`` is specified,
        the value type is converted to the chosen type."""
        return self.get_graph().copy_property(self, value_type=value_type)
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    def __copy__(self):
        return self.copy()

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    def get_graph(self):
        """Get the graph class to which the map refers."""
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        g = self.__g()
        if g is None:
            g = self.__base_g()
        return g
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    def key_type(self):
        """Return the key type of the map. Either 'g', 'v' or 'e'."""
        return self.__key_type

    def value_type(self):
        """Return the value type of the map."""
        return self.__map.value_type()

    def python_value_type(self):
        """Return the python-compatible value type of the map."""
        return _python_type(self.__map.value_type())

    def get_array(self):
        """Get a :class:`~graph_tool.PropertyArray` with the property values.

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        .. note::

           An array is returned *only if* the value type of the property map is
           a scalar. For vector, string or object types, ``None`` is returned
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           instead. For vector and string objects, indirect array access is
           provided via the :func:`~graph_tool.PropertyMap.get_2d_array()` and
           :func:`~graph_tool.PropertyMap.set_2d_array()` member functions.
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        .. warning::
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           The returned array does not own the data, which belongs to the
           property map. Therefore, if the graph changes, the array may become
           *invalid* and any operation on it will fail with a
           :class:`ValueError` exception. Do **not** store the array if
           the graph is to be modified; store a **copy** instead.
        """
        a = self._get_data()
        if a is None:
            return None
        return PropertyArray(a, prop_map=self)

    def _get_data(self):
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        g = self.get_graph()
        if g is None:
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            return None
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        if g.get_edge_filter() is not None or g.get_vertex_filter() is not None:
            u = GraphView(g, skip_properties=True, skip_efilt=True,
                          skip_vfilt=True)
        else:
            u = g
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        if self.__key_type == 'v':
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            n = u.num_vertices()
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        elif self.__key_type == 'e':
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            n = max(u.max_edge_index, 1)
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        else:
            n = 1
        a = self.__map.get_array(n)
        return a

    def __set_array(self, v):
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        a = self.get_array()
        if a is None:
            return
        a[:] = v
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    a = property(get_array, __set_array,
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                 doc=r"""Shortcut to the :meth:`~PropertyMap.get_array` method
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                 as an attribute. This makes assignments more convenient, e.g.:

                 >>> g = gt.Graph()
                 >>> g.add_vertex(10)
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                 <...>
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                 >>> prop = g.new_vertex_property("double")
                 >>> prop.a = np.random.random(10)           # Assignment from array
                 """)

    def __get_set_f_array(self, v=None, get=True):
        g = self.get_graph()
        if g is None:
            return None
        a = self.get_array()
        filt = [None]
        if self.__key_type == 'v':
            filt = g.get_vertex_filter()
        elif self.__key_type == 'e':
            filt = g.get_edge_filter()
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            if g.get_vertex_filter()[0] is not None:
                filt = (g.new_edge_property("bool"), filt[1])
                u = GraphView(g, directed=True, skip_properties=True)
                libcore.mark_edges(u._Graph__graph, _prop("e", g, filt[0]))
                if filt[1]:
                    filt[0].a = 1 - filt[0].a
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        if get:
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            if a is None:
                return a
            if filt[0] is None:
                return a
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            return a[filt[0].a == (not filt[1])]
        else:
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            if a is None:
                return
            if filt[0] is None:
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                try:
                    a[:] = v
                except ValueError:
                    a[:] = v[:len(a)]
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            else:
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                m = filt[0].a == (not filt[1])
                try:
                    a[m] = v
                except ValueError:
                    a[m] = v[:len(m)][m]
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    fa = property(__get_set_f_array,
                  lambda self, v: self.__get_set_f_array(v, False),
                  doc=r"""The same as the :attr:`~PropertyMap.a` attribute, but
                  instead an *indexed* array is returned, which contains only
                  entries for vertices/edges which are not filtered out. If
                  there are no filters in place, the array is not indexed, and
                  is identical to the :attr:`~PropertyMap.a` attribute.

                  Note that because advanced indexing is triggered, a **copy**
                  of the array is returned, not a view, as for the
                  :attr:`~PropertyMap.a` attribute. Nevertheless, the assignment
                  of values to the *whole* array at once works as expected.""")

    def __get_set_m_array(self, v=None, get=True):
        g = self.get_graph()
        if g is None:
            return None
        a = self.get_array()
        filt = [None]
        if self.__key_type == 'v':
            filt = g.get_vertex_filter()
        elif self.__key_type == 'e':
            filt = g.get_edge_filter()
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            if g.get_vertex_filter()[0] is not None:
                filt = (g.new_edge_property("bool"), filt[1])
                u = GraphView(g, directed=True, skip_properties=True)
                libcore.mark_edges(u._Graph__graph, _prop("e", g, filt[0]))
                if filt[1]:
                    filt[0].a = 1 - filt[0].a
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        if filt[0] is None or a is None:
            if get:
                return a
            else:
                return
        ma = numpy.ma.array(a, mask=(filt[0].a == False) if not filt[1] else (filt[0].a == True))
        if get:
            return ma
        else:
            ma[:] = v

    ma = property(__get_set_m_array,
                  lambda self, v: self.__get_set_m_array(v, False),
                  doc=r"""The same as the :attr:`~PropertyMap.a` attribute, but
                  instead a :class:`~numpy.ma.MaskedArray` object is returned,
                  which contains only entries for vertices/edges which are not
                  filtered out. If there are no filters in place, a regular
                  :class:`~graph_tool.PropertyArray` is returned, which is
                  identical to the :attr:`~PropertyMap.a` attribute.""")
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    def get_2d_array(self, pos):
        r"""Return a two-dimensional array with a copy of the entries of the
        vector-valued property map. The parameter ``pos`` must be a sequence of
        integers which specifies the indexes of the property values which will
        be used. """

        if self.key_type() == "g":
            raise ValueError("Cannot create multidimensional array for graph property maps.")
        if "vector" not in self.value_type() and (len(pos) > 1 or pos[0] != 0):
            raise ValueError("Cannot create array of dimension %d (indexes %s) from non-vector property map of type '%s'." \
                             % (len(pos), str(pos), self.value_type()))
        if "string" in self.value_type():
            if "vector" in self.value_type():
                p = ungroup_vector_property(self, pos)
            else:
                p = [self]
            g = self.get_graph()
            if self.key_type() == "v":
                N = g.num_vertices()
            else:
                N = g.num_edges()
            a = [["" for j in range(N)] for i in range(len(p))]
            if self.key_type() == "v":
                iters = g.vertices()
            else:
                iters = g.edges()
            for v in iters:
                for i in range(len(p)):
                    a[i][int(v)] = p[i][v]
            if len(a) == 1:
                a = a[0]
            return numpy.array(a)
        a = self.fa
        if a is not None:
            return numpy.array(a)
        else:
            p = ungroup_vector_property(self, pos)
            return numpy.array([x.a for x in p])

    def set_2d_array(self, a, pos=None):
        r"""Set the entries of the vector-valued property map from a
        two-dimensional array ``a``. If given, the parameter ``pos`` must be a
        sequence of integers which specifies the indexes of the property values
        which will be set."""

        if self.key_type() == "g":
            raise ValueError("Cannot set multidimensional array for graph property maps.")
        if "vector" not in self.value_type():
            if len(a.shape) != 1:
                raise ValueError("Cannot set array of shape %s to non-vector property map of type %s" % \
                                 (str(a.shape), self.value_type()))
            if self.value_type() != "string":
                self.fa = a
            else:
                g = self.get_graph()
                if self.key_type() == "v":
                    iters = g.vertices()
                else:
                    iters = g.edges()
                for i, v in enumerate(iters):
                    self[v] = a[i]
            return

        val = self.value_type()[7:-1]
        ps = []
        for i in range(a.shape[0]):
            ps.append(self.get_graph().new_property(self.key_type(), val))
            if self.value_type() != "string":
                ps[-1].fa = a[i]
            else:
                g = self.get_graph()
                if self.key_type() == "v":
                    iters = g.vertices()
                else:
                    iters = g.edges()
                for j, v in enumerate(iters):
                    ps[-1][v] = a[i, j]
        group_vector_property(ps, val, self, pos)

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    def is_writable(self):
        """Return True if the property is writable."""
        return self.__map.is_writable()

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    def __call__(self, a):
        p = self.copy()
        p.fa = a
        return p

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def _check_prop_writable(prop, name=None):
    if not prop.is_writable():
        raise ValueError("property map%s is not writable." %\
                         ((" '%s'" % name) if name != None else ""))


def _check_prop_scalar(prop, name=None, floating=False):
    scalars = ["bool", "int32_t", "int64_t", "unsigned long",
               "double", "long double"]
    if floating:
        scalars = ["double", "long double"]

    if prop.value_type() not in scalars:
        raise ValueError("property map%s is not of scalar%s type." %\
                         (((" '%s'" % name) if name != None else ""),
                          (" floating" if floating else "")))


def _check_prop_vector(prop, name=None, scalar=True, floating=False):
    scalars = ["bool", "int32_t", "int64_t", "unsigned long",
               "double", "long double"]
    if not scalar:
        scalars += ["string"]
    if floating:
        scalars = ["double", "long double"]
    vals = ["vector<%s>" % v for v in scalars]
    if prop.value_type() not in vals:
        raise ValueError("property map%s is not of vector%s type." %\
                         (((" '%s'" % name) if name != None else ""),
                          (" floating" if floating else "")))


def group_vector_property(props, value_type=None, vprop=None, pos=None):
    """Group list of properties ``props`` into a vector property map of the same type.

    Parameters
    ----------
    props : list of :class:`~graph_tool.PropertyMap`
        Properties to be grouped.
    value_type : string (optional, default: None)
        If supplied, defines the value type of the grouped property.
    vprop : :class:`~graph_tool.PropertyMap` (optional, default: None)
        If supplied, the properties are grouped into this property map.
    pos : list of ints (optional, default: None)
        If supplied, should contain a list of indexes where each corresponding
        element of ``props`` should be inserted.

    Returns
    -------
    vprop : :class:`~graph_tool.PropertyMap`
       A vector property map with the grouped values of each property map in
       ``props``.
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    Examples
    --------
    >>> from numpy.random import seed, randint
    >>> from numpy import array
    >>> seed(42)
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    >>> gt.seed_rng(42)
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    >>> g = gt.random_graph(100, lambda: (3, 3))
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    >>> props = [g.new_vertex_property("int") for i in range(3)]
    >>> for i in range(3):
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    ...    props[i].a = randint(0, 100, g.num_vertices())
    >>> gprop = gt.group_vector_property(props)
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    >>> print(gprop[g.vertex(0)].a)
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    [51 25  8]
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    >>> print(array([p[g.vertex(0)] for p in props]))
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    [51 25  8]
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    """
    g = props[0].get_graph()
    vtypes = set()
    keys = set()
    for i, p in enumerate(props):
        if "vector" in p.value_type():
            raise ValueError("property map 'props[%d]' is a vector property." %
                             i)
        vtypes.add(p.value_type())
        keys.add(p.key_type())
    if len(keys) > 1:
        raise ValueError("'props' must be of the same key type.")
    k = keys.pop()

    if vprop == None:
        if value_type == None and len(vtypes) == 1:
            value_type = vtypes.pop()

        if value_type != None:
            value_type = "vector<%s>" % value_type
            if k == 'v':
                vprop = g.new_vertex_property(value_type)
            elif k == 'e':
                vprop = g.new_edge_property(value_type)
            else:
                vprop = g.new_graph_property(value_type)
        else:
            ValueError("Can't automatically determine property map value" +
                       " type. Please provide the 'value_type' parameter.")
    _check_prop_vector(vprop, name="vprop", scalar=False)

    for i, p in enumerate(props):
        if k != "g":
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            u = GraphView(g, directed=True, reversed=g.is_reversed(),
                          skip_properties=True)
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            libcore.group_vector_property(u._Graph__graph, _prop(k, g, vprop),
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                                          _prop(k, g, p),
                                          i if pos == None else pos[i],
                                          k == 'e')
        else:
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            vprop[g][i if pos is None else pos[i]] = p[g]
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    return vprop


def ungroup_vector_property(vprop, pos, props=None):
    """Ungroup vector property map ``vprop`` into a list of individual property maps.

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    Parameters
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    ----------
    vprop : :class:`~graph_tool.PropertyMap`
        Vector property map to be ungrouped.
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    pos : list of ints
        A list of indexes corresponding to where each element of ``vprop``
        should be inserted into the ungrouped list.
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    props : list of :class:`~graph_tool.PropertyMap`  (optional, default: None)
        If supplied, should contain a list of property maps to which ``vprop``
        should be ungroupped.

    Returns
    -------
    props : list of :class:`~graph_tool.PropertyMap`
       A list of property maps with the ungrouped values of ``vprop``.
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    Examples
    --------
    >>> from numpy.random import seed, randint
    >>> from numpy import array
    >>> seed(42)
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    >>> gt.seed_rng(42)
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    >>> g = gt.random_graph(100, lambda: (3, 3))
    >>> prop = g.new_vertex_property("vector<int>")
    >>> for v in g.vertices():
    ...    prop[v] = randint(0, 100, 3)
    >>> uprops = gt.ungroup_vector_property(prop, [0, 1, 2])
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    >>> print(prop[g.vertex(0)].a)
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    [51 92 14]
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    >>> print(array([p[g.vertex(0)] for p in uprops]))
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    [51 92 14]
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    """

    g = vprop.get_graph()
    _check_prop_vector(vprop, name="vprop", scalar=False)
    k = vprop.key_type()
    value_type = vprop.value_type().split("<")[1].split(">")[0]
    if props == None:
        if k == 'v':
            props = [g.new_vertex_property(value_type) for i in pos]
        elif k == 'e':
            props = [g.new_edge_property(value_type) for i in pos]
        else:
            props = [g.new_graph_property(value_type) for i in pos]

    for i, p in enumerate(pos):
        if props[i].key_type() != k:
            raise ValueError("'props' must be of the same key type as 'vprop'.")

        if k != 'g':
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            u = GraphView(g, directed=True, reversed=g.is_reversed(),
                          skip_properties=True)
            libcore.ungroup_vector_property(u._Graph__graph,
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                                            _prop(k, g, vprop),
                                            _prop(k, g, props[i]),
                                            p, k == 'e')
        else:
            if len(vprop[g]) <= pos[i]:
                vprop[g].resize(pos[i] + 1)
            props[i][g] = vprop[g][pos[i]]
    return props


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def infect_vertex_property(g, prop, vals=None):
    """Propagate the `prop` values of vertices with value `val` to all their
    out-neighbours.

    Parameters
    ----------
    prop : :class:`~graph_tool.PropertyMap`
        Property map to be modified.
    vals : list (optional, default: `None`)
        List of values to be propagated. If not provided, all values
        will be propagated.

    Returns
    -------
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    None : ``None``
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    Examples
    --------
    >>> from numpy.random import seed
    >>> seed(42)
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    >>> gt.seed_rng(42)
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    >>> g = gt.random_graph(100, lambda: (3, 3))
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    >>> prop = g.vertex_index.copy("int32_t")
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    >>> gt.infect_vertex_property(g, prop, [10])
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    >>> print(sum(prop.a == 10))
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    """
    libcore.infect_vertex_property(g._Graph__graph, _prop("v", g, prop),
                                   vals)

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def edge_difference(g, prop, ediff=None):
    """Return an edge property map corresponding to the difference between the
    values of `prop` of target and source vertices of each edge.

    Parameters
    ----------
    prop : :class:`~graph_tool.PropertyMap`
        Vertex property map to be used to compute the difference..
    ediff : :class:`~graph_tool.PropertyMap` (optional, default: `None`)
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        If provided, the difference values will be stored in this property map.
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    Returns
    -------
    ediff : :class:`~graph_tool.PropertyMap`
        Edge differences.

    Examples
    --------
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    >>> gt.seed_rng(42)
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    >>> g = gt.random_graph(100, lambda: (3, 3))
    >>> ediff = gt.edge_difference(g, g.vertex_index)
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    >>> print(ediff.a)
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    [ 63  74  70 -19   1 -41 -54 -38 -68 -87 -85 -40 -41  -6  -3   4  12 -40
      -1   1 -47 -31 -49 -39  28 -37 -50 -32 -34 -12  -1  -4   5  10   8 -51
     -27  18  -3  45 -13  42   3 -31  25 -21  44 -28 -34  53  -5  -7  47 -26
      67   7  28 -24  30  50  24  39  43  45  64  78  74  84  -7  32  73  47
      34  70   2  -2 -78 -92  81  22  80  37  66  -2   1  26  95  26  62  66
      30   7  56  79  69  80  74  84   8  47  73  54  11  79  71  60  72  57
      41 -15  33 -15 -28  -4 -29 -13  -8 -40  -6   6 -19 -22  15  10  -7 -13
     -29 -10  32  -9 -30 -14 -63 -60  -2 -13 -39  10  12  14 -37 -29 -16 -65
       1 -52 -21 -49 -43 -57  54  31  62 -40 -66 -53 -12 -71 -92 -18 -49 -65
     -83 -80 -33 -67 -70 -58 -40 -53 -44 -71 -46 -75 -37 -44 -57  -3 -15 -76
       4  16 -55 -10   1 -33  16  -6  -7 -66 -49 -57 -58 -35 -32  20 -28 -58
       9  28   7 -67  29   6 -17 -54  -8 -31  24 -37 -29 -19  -5 -13  17 -39
     -25  17  25  62  65 -17  34  -7  12   3  17 -13  -5  40  74  80  36  73
      75  52   4  75  67  43  17  33  57  44  40  34 -26 -15  -5  31  30  51
     -17  21   5 -19  34  -1  12  -1  62 -27  33 -22  43 -22 -39  33 -24  41
     -37  17 -31  45 -40 -39 -36  49  16  36 -19  44  36 -51 -35 -13   4  14
     -44 -16  -8 -13   9 -29  10 -62 -26 -47 -44   3]
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    """
    val_t = prop.value_type()
    if val_t == "unsigned long":
        val_t = "int32_t"
    if ediff is None:
        ediff = g.new_edge_property(val_t)
    if ediff.value_type() != val_t:
        raise ValueError("'ediff' must be of the same value type as 'prop': " +
                         val_t)
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    if not g.is_directed():
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        g = GraphView(g, directed=True, skip_properties=True)
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    libcore.edge_difference(g._Graph__graph, _prop("v", g, prop),
                            _prop("e", g, ediff))
    return ediff


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class PropertyDict(dict):
    """Wrapper for the dict of vertex, graph or edge properties, which sets the
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    value on the property map when changed in the dict.

    .. note::

        The class is only an one-way proxy to the internally-kept properties. If
        you modify this object, the change will be propagated to the internal
        dictionary, but not vice-versa. Keep this in mind if you intend to keep
        a copy of the class instance.
    """
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    def __init__(self, g, old, get_func, set_func, del_func):
        dict.__init__(self)
        dict.update(self, old)
        self.g = g
        self.get_func = get_func
        self.set_func = set_func
        self.del_func = del_func

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    def __getitem__(self, key):
        if self.get_func != None:
            val = self.get_func(self.g, key)
            dict.__setitem__(self, key, val)
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            return val
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        else:
            raise KeyError("Property dict cannot be gotten")

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    def __setitem__(self, key, val):
        if self.set_func != None:
            self.set_func(self.g, key, val)
        else:
            raise KeyError("Property dict cannot be set")
        dict.__setitem__(self, key, val)

    def __delitem__(self, key):
        self.del_func(self.g, key)
        dict.__delitem__(self, key)

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    def clear(self):
        for k in self.keys():
            self.del_func(self.g, k)
        dict.clear(self)

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################################################################################
# Graph class
# The main graph interface
################################################################################

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from .libgraph_tool_core import Vertex, EdgeBase, Vector_bool, Vector_int16_t, \
    Vector_int32_t, Vector_int64_t, Vector_double, Vector_long_double, \
    Vector_string, new_vertex_property, new_edge_property, new_graph_property
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class Graph(object):
    """Generic multigraph class.

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    This class encapsulates either a directed multigraph (default or if
    ``directed=True``) or an undirected multigraph (if ``directed=False``),
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    with optional internal edge, vertex or graph properties.
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    If ``g`` is specified, the graph (and its internal properties) will be
    copied.

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    If ``prune`` is set to ``True``, and ``g`` is specified, only the filtered
    graph will be copied, and the new graph object will not be
    filtered. Optionally, a tuple of three booleans can be passed as value to
    ``prune``, to specify a different behavior to vertex, edge, and reversal
    filters, respectively.
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    If ``vorder`` is specified, it should correspond to a vertex
    :class:`~graph_tool.PropertyMap` specifying the ordering of the vertices in
    the copied graph.

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    The graph is implemented as an `adjacency list`_, where both vertex and edge
    lists are C++ STL vectors.

    .. _adjacency list: http://en.wikipedia.org/wiki/Adjacency_list

    """

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    def __init__(self, g=None, directed=True, prune=False, vorder=None):
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        self.__properties = {}
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        self.__known_properties = {}
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        self.__filter_state = {"reversed": False,
                               "edge_filter": (None, False),
                               "vertex_filter": (None, False),
                               "directed": True}
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        if g is None:
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            self.__graph = libcore.GraphInterface()
            self.set_directed(directed)
        else:
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            if isinstance(prune, bool):
                vprune = eprune = rprune = prune
            else:
                vprune, eprune, rprune = prune
            if not (vprune or eprune or rprune):
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                gv = GraphView(g, skip_vfilt=True,
                               skip_efilt=True)
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                if not rprune:
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                    gv.set_reversed(False)
            else:
                gv = g

            # The filters may or may not not be in the internal property maps
            vfilt = g.get_vertex_filter()[0]
            efilt = g.get_edge_filter()[0]
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            if (vorder is None and
                ((g.get_vertex_filter()[0] is None and g.get_edge_filter()[0] is None) or
                 (not vprune and not eprune))):
                # Do a simpler, faster copy.
                self.__graph = libcore.GraphInterface(gv.__graph, False,
                                                      [], [], None)
                nvfilt = nefilt = None
                for k, m in g.properties.items():
                    nmap = self.copy_property(m, g=gv)
                    self.properties[k] = nmap
                    if m is vfilt:
                        nvfilt = nmap
                    if m is efilt:
                        nefilt = nmap
                if vfilt is not None:
                    if nvfilt is None:
                        nvfilt = self.copy_property(vfilt, g=gv)
                    self.set_vertex_filter(nvfilt, g.get_vertex_filter()[1])
                if efilt is not None:
                    if nefilt is None:
                        nefilt = self.copy_property(efilt, g=gv)
                    self.set_edge_filter(nefilt, g.get_edge_filter()[1])
            else:

                # Copy all internal properties from original graph.
                vprops = []
                eprops = []
                ef_pos = vf_pos = None
                for k, m in gv.vertex_properties.items():
                    if not vprune and m is vfilt:
                        vf_pos = len(vprops)
                    vprops.append([_prop("v", gv, m), libcore.any()])
                for k, m in gv.edge_properties.items():
                    if not eprune and  m is efilt:
                        ef_pos = len(eprops)
                    eprops.append([_prop("e", gv, m), libcore.any()])
                if not vprune and vf_pos is None and vfilt is not None:
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                    vf_pos = len(vprops)
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                    vprops.append([_prop("v", gv, vfilt), libcore.any()])
                if not eprune and ef_pos is None and efilt is not None:
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                    ef_pos = len(eprops)
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                    eprops.append([_prop("e", gv, efilt), libcore.any()])

                # The vertex ordering
                if vorder is None:
                    vorder = gv.new_vertex_property("int")
                    vorder.fa = numpy.arange(gv.num_vertices())

                # The actual copying of the graph and property maps
                self.__graph = libcore.GraphInterface(gv.__graph, False,
                                                      vprops,
                                                      eprops,
                                                      _prop("v", gv, vorder))

                # Put the copied properties in the internal dictionary
                for i, (k, m) in enumerate(g.vertex_properties.items()):
                    pmap = new_vertex_property(m.value_type(),
                                               self.__graph.GetVertexIndex(),
                                               vprops[i][1])
                    self.vertex_properties[k] = PropertyMap(pmap, self, "v")

                for i, (k, m) in enumerate(g.edge_properties.items()):
                    pmap = new_edge_property(m.value_type(),
                                             self.__graph.GetEdgeIndex(),
                                             eprops[i][1])
                    self.edge_properties[k] = PropertyMap(pmap, self, "e")

                for k, v in g.graph_properties.items():
                    new_p = self.new_graph_property(v.value_type())
                    new_p[self] = v[g]
                    self.graph_properties[k] = new_p

                if vf_pos is not None:
                    pmap = new_vertex_property("bool",
                                               self.__graph.GetVertexIndex(),
                                               vprops[vf_pos][1])
                    pmap = PropertyMap(pmap, self, "v")
                    self.set_vertex_filter(pmap, g.get_vertex_filter()[1])
                if ef_pos is not None:
                    pmap = new_edge_property("bool",
                                             self.__graph.GetEdgeIndex(),
                                             eprops[ef_pos][1])
                    pmap = PropertyMap(pmap, self, "e")
                    self.set_edge_filter(pmap, g.get_edge_filter()[1])
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            if not rprune:
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                self.set_reversed(g.is_reversed())
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            # directedness is always a filter
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            self.set_directed(g.is_directed())
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        # internal index maps
        self.__vertex_index = \
                 PropertyMap(libcore.get_vertex_index(self.__graph), self, "v")
        self.__edge_index = \
                 PropertyMap(libcore.get_edge_index(self.__graph), self, "e")

        # modification permissions
        self.__perms = {"add_edge": True, "del_edge": True,
                        "add_vertex": True, "del_vertex": True}

    def copy(self):
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        """Return a deep copy of self. All :ref:`internal property maps <sec_internal_props>`
        are also copied."""
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        return Graph(self)

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    def __copy__(self):
        return self.copy()

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    def __repr__(self):
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        # provide more useful information
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        d = "directed" if self.is_directed() else "undirected"
        fr = ", reversed" if self.is_reversed() and self.is_directed() else ""
        f = ""
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        if self.get_edge_filter()[0] is not None:
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            f += ", edges filtered by %s" % (str(self.get_edge_filter()))
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        if self.get_vertex_filter()[0] is not None:
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            f += ", vertices filtered by %s" % (str(self.get_vertex_filter()))
        n = self.num_vertices()
        e = self.num_edges()
        return "<%s object, %s%s, with %d %s and %d edge%s%s at 0x%x>"\
               % (type(self).__name__, d, fr, n,
                  "vertex" if n == 1 else "vertices", e, "" if e == 1 else "s",
                  f, id(self))

    # Graph access
    # ============

    def __check_perms(self, ptype):
        if not self.__perms[ptype]:
            raise RuntimeError("the graph cannot be modified at this point!")

    def vertices(self):
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        """Return an :meth:`iterator <iterator.__iter__>` over the vertices.

        .. note::

           The order of the vertices traversed by the iterator **always**
           corresponds to the vertex index ordering, as given by the
           :attr:`~graph_tool.Graph.vertex_index` property map.
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        Examples
        --------
        >>> g = gt.Graph()
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        >>> vlist = list(g.add_vertex(5))
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        >>> vlist2 = []
        >>> for v in g.vertices():
        ...     vlist2.append(v)
        ...
        >>> assert(vlist == vlist2)

        """
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        return libcore.get_vertices(weakref.ref(self))
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    def vertex(self, i, use_index=True):
        """Return the vertex with index ``i``. If ``use_index=False``, the
        ``i``-th vertex is returned (which can differ from the vertex with index
        ``i`` in case of filtered graphs). """
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        vfilt = self.get_vertex_filter()
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        try:
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            if use_index:
                self.set_vertex_filter(None)
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            v = libcore.get_vertex(weakref.ref(self), int(i))
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        finally:
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            self.set_vertex_filter(vfilt[0], vfilt[1])
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        return v

    def edge(self, s, t, all_edges=False):
        """Return the edge from vertex ``s`` to ``t``, if it exists. If
        ``all_edges=True`` then a list is returned with all the parallel edges
        from ``s`` to ``t``, otherwise only one edge is returned.

        This operation will take :math:`O(k(s))` time, where :math:`k(s)` is the
        out-degree of vertex :math:`s`.
        """
        s = self.vertex(int(s))
        t = self.vertex(int(t))
        edges = []
        for e in s.out_edges():
            if e.target() == t:
                if not all_edges:
                    return e
                edges.append(e)
        if all_edges:
            return edges
        return None

    def edges(self):
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        """Return an :meth:`iterator <iterator.__iter__>` over the edges.

        .. note::

           The order of the edges traversed by the iterator **does not**
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           necessarily correspond to the edge index ordering, as given by the
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           :attr:`~graph_tool.Graph.edge_index` property map. This will only
           happen after :meth:`~graph_tool.Graph.reindex_edges` is called, or in
           certain situations such as just after a graph is loaded from a
           file. However, further manipulation of the graph may destroy the
           ordering.

        """
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        return libcore.get_edges(weakref.ref(self))
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    def add_vertex(self, n=1):
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        """Add a vertex to the graph, and return it. If ``n != 1``, ``n``
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        vertices are inserted and an iterator over the new vertices is returned.
        This operation is :math:`O(n)`.
        """
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        if n == 0:
            return (None for i in range(0, 0))

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        self.__check_perms("add_vertex")
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        v = libcore.add_vertex(weakref.ref(self), n)

        if n <= 1:
            return v
        else:
            pos = self.num_vertices() - n
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            return (self.vertex(i) for i in range(pos, pos + n))
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    def remove_vertex(self, vertex, fast=False):
        r"""Remove a vertex from the graph.

        .. note::

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           If the option ``fast == False`` is given, this operation is
           :math:`O(N + E)` (this is the default). Otherwise it is
           :math:`O(k + k_{\text{last}})`, where :math:`k` is the (total)
           degree of the vertex being deleted, and :math:`k_{\text{last}}` is
           the (total) degree of the vertex with the largest index.
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        .. warning::

           If ``fast == True``, the vertex being deleted is 'swapped' with the
           last vertex (i.e. with the largest index), which will in turn inherit
           the index of the vertex being deleted. All property maps associated
           with the graph will be properly updated, but the index ordering of
           the graph will no longer be the same.

        """
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        self.__check_perms("del_vertex")
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        vertex = self.vertex(int(vertex))
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        index = self.vertex_index[vertex]
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        u = GraphView(self, skip_properties=True, skip_vfilt=True)
        back = u.num_vertices() - 1
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        # move / shift all known property maps
        if index != back:
            for pmap in self.__known_properties.values():
                if pmap() is not None and pmap().key_type() == "v" and pmap().is_writable():
                    if fast:
                        self.__graph.MoveVertexProperty(pmap()._PropertyMap__map.get_map(), index)
                    else:
                        self.__graph.ShiftVertexProperty(pmap()._PropertyMap__map.get_map(), index)

        libcore.remove_vertex(self.__graph, vertex, fast)
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    def clear_vertex(self, vertex):
        """Remove all in and out-edges from the given vertex."""
        del_es = set()
        for e in vertex.all_edges():
            del_es.add(e)
        for e in del_es:
            self.remove_edge(e)

    def add_edge(self, source, target):
        """Add a new edge from ``source`` to ``target`` to the graph, and return
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        it. This operation is :math:`O(1)`."""
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        self.__check_perms("add_edge")
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        e = libcore.add_edge(weakref.ref(self), self.vertex(int(source)),
                             self.vertex(int(target)))
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        efilt = self.get_edge_filter()
        if efilt[0] is not None:
            efilt[0][e] = not efilt[1]
        return e
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    def remove_edge(self, edge):
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        r"""Remove an edge from the graph.

        .. note::

           This operation is normally :math:`O(k_s + k_t)`, where :math:`k_s`
           and :math:`k_s` are the total degrees of the source and target
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           vertices, respectively. However, if :meth:`~Graph.set_fast_edge_removal`
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           is set to `True`, this operation becomes :math:`O(1)`.

        .. warning::

           The relative ordering of the remaining edges in the graph is kept
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           unchanged, unless :meth:`~Graph.set_fast_edge_removal` is set to
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           `True`, in which case it can change.
        """
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        self.__check_perms("del_edge")
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        return libcore.remove_edge(self.__graph, edge)
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    def set_fast_edge_removal(self, fast=True):
        r"""If ``fast == True`` the fast :math:`O(1)` removal of edges will be
        enabled. This requires an additional data structure of size :math:`O(E)`
        to be kept at all times.  If ``fast == False``, this data structure is
        destroyed."""
        self.__graph.SetKeepEpos(fast)

    def get_fast_edge_removal(self):
        r"""Return whether the fast :math:`O(1)` removal of edges is currently
        enabled."""
        return self.__graph.GetKeepEpos()

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    def clear(self):
        """Remove all vertices and edges from the graph."""
        self.__check_perms("del_vertex")
        self.__check_perms("del_edge")
        self.__graph.Clear()

    def clear_edges(self):
        """Remove all edges from the graph."""
        self.__check_perms("del_edge")
        self.__graph.ClearEdges()

    # Internal property maps
    # ======================

    # all properties
    def __get_properties(self):
        return PropertyDict(self, self.__properties,
                            lambda g, k: g.__properties[k],
                            lambda g, k, v: g.__set_property(k[0], k[1], v),
                            lambda g, k: g.__del_property(k[0], k[1]))

    @_limit_args({"t": ["v", "e", "g"]})
    @_require("k", str)
    def __set_property(self, t, k, v):
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        if t == "g" and not isinstance(v, PropertyMap):
            self.__properties[(t, k)][self] = v
        else:
            if t != v.key_type():
                raise ValueError("wrong key type for property map")
            self.__properties[(t, k)] = v
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    @_limit_args({"t": ["v", "e", "g"]})
    @_require("k", str)
    def __del_property(self, t, k):
        del self.__properties[(t, k)]

    properties = property(__get_properties,
                          doc=
    """Dictionary of internal properties. Keys must always be a tuple, where the
    first element if a string from the set {'v', 'e', 'g'}, representing a
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    vertex, edge or graph property, respectively, and the second element is the
    name of the property map.
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    Examples
    --------
    >>> g = gt.Graph()
    >>> g.properties[("e", "foo")] = g.new_edge_property("vector<double>")
    >>> del g.properties[("e", "foo")]
    """)

    def __get_specific_properties(self, t):
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        props = dict([(k[1], v) for k, v in self.__properties.items() \
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                      if k[0] == t])
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        return props

    # vertex properties
    def __get_vertex_properties(self):
        return PropertyDict(self, self.__get_specific_properties("v"),
                            lambda g, k: g.__properties[("v", k)],
                            lambda g, k, v: g.__set_property("v", k, v),
                            lambda g, k: g.__del_property("v", k))
    vertex_properties = property(__get_vertex_properties,
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                                 doc="Dictionary of internal vertex properties. The keys are the property names.")
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    vp = property(__get_vertex_properties,
                  doc="Alias to :attr:`~Graph.vertex_properties`.")
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    # edge properties
    def __get_edge_properties(self):
        return PropertyDict(self, self.__get_specific_properties("e"),
                            lambda g, k: g.__properties[("e", k)],
                            lambda g, k, v: g.__set_property("e", k, v),
                            lambda g, k: g.__del_property("e", k))
    edge_properties = property(__get_edge_properties,
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                                 doc="Dictionary of internal edge properties. The keys are the property names.")
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    ep = property(__get_edge_properties,
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                  doc="Alias to :attr:`~Graph.edge_properties`.")
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    # graph properties
    def __get_graph_properties(self):
        return PropertyDict(self, self.__get_specific_properties("g"),
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                            lambda g, k: g.__properties[("g", k)][g],
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                            lambda g, k, v: g.__set_property("g", k, v),
                            lambda g, k: g.__del_property("g", k))
    graph_properties = property(__get_graph_properties,
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                                 doc="Dictionary of internal graph properties. The keys are the property names.")
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    gp = property(__get_graph_properties,
                  doc="Alias to :attr:`~Graph.graph_properties`.")
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    def own_property(self, prop):
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        """Return a version of the property map 'prop' (possibly belonging to
        another graph) which is owned by the current graph."""
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        return PropertyMap(prop._PropertyMap__map, self, prop.key_type())

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    def list_properties(self):
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        """Print a list of all internal properties.
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        Examples
        --------
        >>> g = gt.Graph()
        >>> g.properties[("e", "foo")] = g.new_edge_property("vector<double>")
        >>> g.vertex_properties["foo"] = g.new_vertex_property("double")
        >>> g.vertex_properties["bar"] = g.new_vertex_property("python::object")
        >>> g.graph_properties["gnat"] = g.new_graph_property("string", "hi there!")
        >>> g.list_properties()
        gnat           (graph)   (type: string, val: hi there!)
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        bar            (vertex)  (type: python::object)
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        foo            (vertex)  (type: double)
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        foo            (edge)    (type: vector<double>)
        """

        if len(self.__properties) == 0:
            return
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        w = max([len(x[0]) for x in list(self.__properties.keys())]) + 4
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        w = w if w > 14 else 14

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        for k, v in self.__properties.items():
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            if k[0] == "g":
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                print("%%-%ds (graph)   (type: %%s, val: %%s)" % w % \
                      (k[1], v.value_type(), str(v[self])))
        for k, v in self.__properties.items():
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            if k[0] == "v":
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                print("%%-%ds (vertex)  (type: %%s)" % w % (k[1],
                                                            v.value_type()))
        for k, v in self.__properties.items():
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            if k[0] == "e":
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                print("%%-%ds (edge)    (type: %%s)" % w % (k[1],
                                                            v.value_type()))
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    # index properties

    def _get_vertex_index(self):
        return self.__vertex_index
    vertex_index = property(_get_vertex_index,
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                            doc="""Vertex index map.

                            It maps for each vertex in the graph an unique
                            integer in the range [0, :meth:`~graph_tool.Graph.num_vertices` - 1].

                            .. note::

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                                Like :attr:`~graph_tool.Graph.edge_index`, this
                                is a special instance of a :class:`~graph_tool.PropertyMap`
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                                class, which is **immutable**, and cannot be
                                accessed as an array.""")
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    def _get_edge_index(self):
        return self.__edge_index
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    edge_index = property(_get_edge_index, doc="""Edge index map.

                            It maps for each edge in the graph an unique
                            integer.

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                            .. note::