Implement 'spectral' module

This includes generations of releated matrices for spectral analysis,
such as the adjacency matrix, laplacian matrix and incidence matrix.

doc/spectral.rst

+.. automodule:: graph_tool.spectral
+   :members:
+   :undoc-members:

src/graph_tool/Makefile.am

@@ -57,3 +57,7 @@ graph_tool_topologydir = $(MOD_DIR)/topology
 graph_tool_flow_PYTHON = \
     flow/__init__.py
 graph_tool_flowdir = $(MOD_DIR)/flow
+
+graph_tool_spectral_PYTHON = \
+    spectral/__init__.py
+graph_tool_spectraldir = $(MOD_DIR)/spectral

src/graph_tool/all.py

@@ -49,5 +49,7 @@ from graph_tool.topology import *
 import graph_tool.topology
 from graph_tool.flow import *
 import graph_tool.flow
+from graph_tool.spectral import *
+import graph_tool.spectral
 from graph_tool.util import *
 import graph_tool.util

src/graph_tool/spectral/__init__.py

+#! /usr/bin/env python
+# graph_tool.py -- a general graph manipulation python module
+#
+# Copyright (C) 2007 Tiago de Paula Peixoto <tiago@forked.de>
+#
+# 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/>.
+
+"""
+``graph_tool.spectral`` - Spectral properties
+---------------------------------------------
+"""
+
+from .. core import _degree, _prop, Graph, _limit_args
+from numpy import *
+import scipy.sparse
+
+
+__all__ = ["adjacency", "laplacian", "incidence"]
+
+def adjacency(g, sparse=True, weight=None):
+    if g.get_vertex_filter()[0] != None:
+        index = g.new_vertex_property("int64_t")
+        for i,v in enumerate(g.vertices()):
+            index[v] = i
+    else:
+        index = g.vertex_index
+    N = g.num_vertices()
+    if sparse:
+        m = scipy.sparse.lil_matrix((N,N))
+    else:
+        m = matrix(zeros((N,N)))
+    for v in g.vertices():
+        for e in v.out_edges():
+            m[index[v],index[e.target()]] = 1 if weight == None else weight[e]
+    if sparse:
+        m = m.tocsr()
+    return m
+
+def _get_deg(v, deg, weight):
+    if deg == "total":
+        if weight == None:
+            d = v.in_degree() + v.out_degree()
+        else:
+            d = sum(weight[e] for e in v.all_edges())
+    elif deg == "in":
+        if weight == None:
+            d = v.in_degree()
+        else:
+            d = sum(weight[e] for e in v.in_edges())
+    else:
+        if weight == None:
+            d = v.out_degree()
+        else:
+            d = sum(weight[e] for e in v.out_edges())
+    return d
+
+@_limit_args({"deg":["total", "in", "out"]})
+def laplacian(g, deg="total", normalized=True, sparse=True, weight=None):
+    if g.get_vertex_filter()[0] != None:
+        index = g.new_vertex_property("int64_t")
+        for i,v in enumerate(g.vertices()):
+            index[v] = i
+    else:
+        index = g.vertex_index
+    N = g.num_vertices()
+    if sparse:
+        m = scipy.sparse.lil_matrix((N,N))
+    else:
+        m = matrix(zeros((N,N)))
+    for v in g.vertices():
+        d = _get_deg(v, deg, weight)
+        if not normalized:
+            m[index[v], index[v]] = d
+        elif d > 0:
+            m[index[v], index[v]] = 1
+        for e in v.out_edges():
+            if not normalized:
+                m[index[v],index[e.target()]] = (-1 if weight == None
+                                                 else -weight[e])
+            else:
+                val = (d*_get_deg(e.target(),deg,weight))**(-0.5)
+                m[index[v],index[e.target()]] = val
+    if sparse:
+        m = m.tocsr()
+    return m
+
+def incidence(g, sparse=True):
+    if g.get_vertex_filter()[0] != None:
+        index = g.new_vertex_property("int64_t")
+        for i,v in enumerate(g.vertices()):
+            index[v] = i
+    else:
+        index = g.vertex_index
+
+    eindex = g.new_edge_property("int64_t")
+    for i, e in enumerate(g.edges()):
+        eindex[e] = i
+
+    N = g.num_vertices()
+    E = g.num_edges()
+    if sparse:
+        m = scipy.sparse.lil_matrix((N,E))
+    else:
+        m = matrix(zeros((N,E)))
+    for v in g.vertices():
+        if g.is_directed():
+            for e in v.out_edges():
+                m[index[v],eindex[e]] += -1
+            for e in v.in_edges():
+                m[index[v],eindex[e]] += 1
+        else:
+            for e in v.out_edges():
+                m[index[v],eindex[e]] += 1
+    if sparse:
+        m = m.tocsr()
+    return m