Source code for networkx.linalg.graphmatrix

"""
Adjacency matrix and incidence matrix of graphs.
"""
#    Copyright (C) 2004-2013 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
import networkx as nx
__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
                        'Pieter Swart (swart@lanl.gov)',
                        'Dan Schult(dschult@colgate.edu)'])

__all__ = ['incidence_matrix',
           'adj_matrix', 'adjacency_matrix',
           ]


[docs]def incidence_matrix(G, nodelist=None, edgelist=None, oriented=False, weight=None): """Return incidence matrix of G. The incidence matrix assigns each row to a node and each column to an edge. For a standard incidence matrix a 1 appears wherever a row's node is incident on the column's edge. For an oriented incidence matrix each edge is assigned an orientation (arbitrarily for undirected and aligning to direction for directed). A -1 appears for the tail of an edge and 1 for the head of the edge. The elements are zero otherwise. Parameters ---------- G : graph A NetworkX graph nodelist : list, optional (default= all nodes in G) The rows are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes(). edgelist : list, optional (default= all edges in G) The columns are ordered according to the edges in edgelist. If edgelist is None, then the ordering is produced by G.edges(). oriented: bool, optional (default=False) If True, matrix elements are +1 or -1 for the head or tail node respectively of each edge. If False, +1 occurs at both nodes. weight : string or None, optional (default=None) The edge data key used to provide each value in the matrix. If None, then each edge has weight 1. Edge weights, if used, should be positive so that the orientation can provide the sign. Returns ------- A : SciPy sparse matrix The incidence matrix of G. Notes ----- For MultiGraph/MultiDiGraph, the edges in edgelist should be (u,v,key) 3-tuples. "Networks are the best discrete model for so many problems in applied mathematics" [1]_. References ---------- .. [1] Gil Strang, Network applications: A = incidence matrix, http://academicearth.org/lectures/network-applications-incidence-matrix """ import scipy.sparse if nodelist is None: nodelist = G.nodes() if edgelist is None: if G.is_multigraph(): edgelist = G.edges(keys=True) else: edgelist = G.edges() A = scipy.sparse.lil_matrix((len(nodelist),len(edgelist))) node_index = dict( (node,i) for i,node in enumerate(nodelist) ) for ei,e in enumerate(edgelist): (u,v) = e[:2] if u == v: continue # self loops give zero column try: ui = node_index[u] vi = node_index[v] except KeyError: raise NetworkXError('node %s or %s in edgelist ' 'but not in nodelist"%(u,v)') if weight is None: wt = 1 else: if G.is_multigraph(): ekey = e[2] wt = G[u][v][ekey].get(weight,1) else: wt = G[u][v].get(weight,1) if oriented: A[ui,ei] = -wt A[vi,ei] = wt else: A[ui,ei] = wt A[vi,ei] = wt return A.asformat('csc')
[docs]def adjacency_matrix(G, nodelist=None, weight='weight'): """Return adjacency matrix of G. Parameters ---------- G : graph A NetworkX graph nodelist : list, optional The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes(). weight : string or None, optional (default='weight') The edge data key used to provide each value in the matrix. If None, then each edge has weight 1. Returns ------- A : SciPy sparse matrix Adjacency matrix representation of G. Notes ----- If you want a pure Python adjacency matrix representation try networkx.convert.to_dict_of_dicts which will return a dictionary-of-dictionaries format that can be addressed as a sparse matrix. For MultiGraph/MultiDiGraph with parallel edges the weights are summed. See to_numpy_matrix for other options. The convention used for self-loop edges in graphs is to assign the diagonal matrix entry value to the edge weight attribute (or the number 1 if the edge has no weight attribute). If the alternate convention of doubling the edge weight is desired the resulting Scipy sparse matrix can be modified as follows: >>> import scipy as sp >>> G = nx.Graph([(1,1)]) >>> A = nx.adjacency_matrix(G) >>> print(A.todense()) [[1]] >>> A.setdiag(A.diagonal()*2) >>> print(A.todense()) [[2]] See Also -------- to_numpy_matrix to_scipy_sparse_matrix to_dict_of_dicts """ return nx.to_scipy_sparse_matrix(G,nodelist=nodelist,weight=weight)
adj_matrix=adjacency_matrix # fixture for nose tests def setup_module(module): from nose import SkipTest try: import scipy except: raise SkipTest("SciPy not available")