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Adjacency matrix and incidence matrix of graphs.
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# Copyright (C) 2004-2011 by
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# Aric Hagberg <hagberg@lanl.gov>
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# Dan Schult <dschult@colgate.edu>
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# Pieter Swart <swart@lanl.gov>
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__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
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'Pieter Swart (swart@lanl.gov)',
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'Dan Schult(dschult@colgate.edu)'])
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__all__ = ['incidence_matrix',
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'adj_matrix', 'adjacency_matrix',
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def incidence_matrix(G, nodelist=None, edgelist=None,
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oriented=False, weight=None):
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"""Return incidence matrix of G.
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The incidence matrix assigns each row to a node and each column to an edge.
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For a standard incidence matrix a 1 appears wherever a row's node is
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incident on the column's edge. For an oriented incidence matrix each
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edge is assigned an orientation (arbitrarily for undirected and aligning to
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direction for directed). A -1 appears for the tail of an edge and 1
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for the head of the edge. The elements are zero otherwise.
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nodelist : list, optional (default= all nodes in G)
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The rows are ordered according to the nodes in nodelist.
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If nodelist is None, then the ordering is produced by G.nodes().
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edgelist : list, optional (default= all edges in G)
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The columns are ordered according to the edges in edgelist.
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If edgelist is None, then the ordering is produced by G.edges().
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oriented: bool, optional (default=False)
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If True, matrix elements are +1 or -1 for the head or tail node
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respectively of each edge. If False, +1 occurs at both nodes.
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weight : string or None, optional (default=None)
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The edge data key used to provide each value in the matrix.
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If None, then each edge has weight 1. Edge weights, if used,
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should be positive so that the orientation can provide the sign.
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The incidence matrix of G.
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For MultiGraph/MultiDiGraph, the edges in edgelist should be
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"Networks are the best discrete model for so many problems in
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applied mathematics" [1]_.
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.. [1] Gil Strang, Network applications: A = incidence matrix,
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http://academicearth.org/lectures/network-applications-incidence-matrix
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"incidence_matrix() requires numpy: http://scipy.org/ ")
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edgelist = G.edges(keys=True)
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A = np.zeros((len(nodelist),len(edgelist)))
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node_index = dict( (node,i) for i,node in enumerate(nodelist) )
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for ei,e in enumerate(edgelist):
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if u == v: continue # self loops give zero column
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raise NetworkXError('node %s or %s in edgelist '
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'but not in nodelist"%(u,v)')
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wt = G[u][v][ekey].get(weight,1)
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wt = G[u][v].get(weight,1)
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return np.asmatrix(A)
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def adjacency_matrix(G, nodelist=None, weight='weight'):
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"""Return adjacency matrix of G.
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nodelist : list, optional
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The rows and columns are ordered according to the nodes in nodelist.
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If nodelist is None, then the ordering is produced by G.nodes().
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weight : string or None, optional (default='weight')
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The edge data key used to provide each value in the matrix.
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If None, then each edge has weight 1.
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Adjacency matrix representation of G.
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If you want a pure Python adjacency matrix representation try
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networkx.convert.to_dict_of_dicts which will return a
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dictionary-of-dictionaries format that can be addressed as a
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For MultiGraph/MultiDiGraph, the edges weights are summed.
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See to_numpy_matrix for other options.
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return nx.to_numpy_matrix(G,nodelist=nodelist,weight=weight)
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adj_matrix=adjacency_matrix
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# fixture for nose tests
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def setup_module(module):
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from nose import SkipTest
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raise SkipTest("NumPy not available")
added
removed
networkx/linalg/graphmatrix.py
