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This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

Source code for networkx.convert_matrix

"""Functions to convert NetworkX graphs to and from numpy/scipy matrices.

The preferred way of converting data to a NetworkX graph is through the
graph constuctor.  The constructor calls the to_networkx_graph() function
which attempts to guess the input type and convert it automatically.

Examples
--------
Create a 10 node random graph from a numpy matrix

>>> import numpy
>>> a = numpy.reshape(numpy.random.random_integers(0,1,size=100),(10,10))
>>> D = nx.DiGraph(a)

or equivalently

>>> D = nx.to_networkx_graph(a,create_using=nx.DiGraph())

See Also
--------
nx_pygraphviz, nx_pydot
"""
#    Copyright (C) 2006-2014 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
import warnings
import networkx as nx
from networkx.convert import _prep_create_using
from networkx.utils import not_implemented_for
__author__ = """\n""".join(['Aric Hagberg <aric.hagberg@gmail.com>',
                           'Pieter Swart (swart@lanl.gov)',
                           'Dan Schult(dschult@colgate.edu)'])
__all__ = ['from_numpy_matrix', 'to_numpy_matrix',
           'to_numpy_recarray',
           'from_scipy_sparse_matrix', 'to_scipy_sparse_matrix']

[docs]def to_numpy_matrix(G, nodelist=None, dtype=None, order=None, multigraph_weight=sum, weight='weight', nonedge=0.0): """Return the graph adjacency matrix as a NumPy matrix. Parameters ---------- G : graph The NetworkX graph used to construct the NumPy matrix. 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(). dtype : NumPy data type, optional A valid single NumPy data type used to initialize the array. This must be a simple type such as int or numpy.float64 and not a compound data type (see to_numpy_recarray) If None, then the NumPy default is used. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. If None, then the NumPy default is used. multigraph_weight : {sum, min, max}, optional An operator that determines how weights in multigraphs are handled. The default is to sum the weights of the multiple edges. weight : string or None optional (default='weight') The edge attribute that holds the numerical value used for the edge weight. If an edge does not have that attribute, then the value 1 is used instead. nonedge : float (default=0.0) The matrix values corresponding to nonedges are typically set to zero. However, this could be undesirable if there are matrix values corresponding to actual edges that also have the value zero. If so, one might prefer nonedges to have some other value, such as nan. Returns ------- M : NumPy matrix Graph adjacency matrix See Also -------- to_numpy_recarray, from_numpy_matrix Notes ----- The matrix entries are assigned to the weight edge attribute. When an edge does not have a weight attribute, the value of the entry is set to the number 1. For multiple (parallel) edges, the values of the entries are determined by the 'multigraph_weight' paramter. The default is to sum the weight attributes for each of the parallel edges. When `nodelist` does not contain every node in `G`, the matrix is built from the subgraph of `G` that is induced by the nodes in `nodelist`. The convention used for self-loop edges in graphs is to assign the diagonal matrix entry value to the weight attributr of the edge (or the number 1 if the edge has no weight attribute). If the alternate convention of doubling the edge weight is desired the resulting Numpy matrix can be modified as follows: >>> import numpy as np >>> G = nx.Graph([(1,1)]) >>> A = nx.to_numpy_matrix(G) >>> A matrix([[ 1.]]) >>> A.A[np.diag_indices_from(A)] *= 2 >>> A matrix([[ 2.]]) Examples -------- >>> G = nx.MultiDiGraph() >>> G.add_edge(0,1,weight=2) >>> G.add_edge(1,0) >>> G.add_edge(2,2,weight=3) >>> G.add_edge(2,2) >>> nx.to_numpy_matrix(G, nodelist=[0,1,2]) matrix([[ 0., 2., 0.], [ 1., 0., 0.], [ 0., 0., 4.]]) """ import numpy as np if nodelist is None: nodelist = G.nodes() nodeset = set(nodelist) if len(nodelist) != len(nodeset): msg = "Ambiguous ordering: `nodelist` contained duplicates." raise nx.NetworkXError(msg) nlen=len(nodelist) undirected = not G.is_directed() index=dict(zip(nodelist,range(nlen))) # Initially, we start with an array of nans. Then we populate the matrix # using data from the graph. Afterwards, any leftover nans will be # converted to the value of `nonedge`. Note, we use nans initially, # instead of zero, for two reasons: # # 1) It can be important to distinguish a real edge with the value 0 # from a nonedge with the value 0. # # 2) When working with multi(di)graphs, we must combine the values of all # edges between any two nodes in some manner. This often takes the # form of a sum, min, or max. Using the value 0 for a nonedge would # have undesirable effects with min and max, but using nanmin and # nanmax with initially nan values is not problematic at all. # # That said, there are still some drawbacks to this approach. Namely, if # a real edge is nan, then that value is a) not distinguishable from # nonedges and b) is ignored by the default combinator (nansum, nanmin, # nanmax) functions used for multi(di)graphs. If this becomes an issue, # an alternative approach is to use masked arrays. Initially, every # element is masked and set to some `initial` value. As we populate the # graph, elements are unmasked (automatically) when we combine the initial # value with the values given by real edges. At the end, we convert all # masked values to `nonedge`. Using masked arrays fully addresses reason 1, # but for reason 2, we would still have the issue with min and max if the # initial values were 0.0. Note: an initial value of +inf is appropriate # for min, while an initial value of -inf is appropriate for max. When # working with sum, an initial value of zero is appropriate. Ideally then, # we'd want to allow users to specify both a value for nonedges and also # an initial value. For multi(di)graphs, the choice of the initial value # will, in general, depend on the combinator function---sensible defaults # can be provided. if G.is_multigraph(): # Handle MultiGraphs and MultiDiGraphs M = np.zeros((nlen, nlen), dtype=dtype, order=order) + np.nan # use numpy nan-aware operations operator={sum:np.nansum, min:np.nanmin, max:np.nanmax} try: op=operator[multigraph_weight] except: raise ValueError('multigraph_weight must be sum, min, or max') for u,v,attrs in G.edges_iter(data=True): if (u in nodeset) and (v in nodeset): i, j = index[u], index[v] e_weight = attrs.get(weight, 1) M[i,j] = op([e_weight, M[i,j]]) if undirected: M[j,i] = M[i,j] else: # Graph or DiGraph, this is much faster than above M = np.zeros((nlen,nlen), dtype=dtype, order=order) + np.nan for u,nbrdict in G.adjacency_iter(): for v,d in nbrdict.items(): try: M[index[u],index[v]] = d.get(weight,1) except KeyError: # This occurs when there are fewer desired nodes than # there are nodes in the graph: len(nodelist) < len(G) pass M[np.isnan(M)] = nonedge M = np.asmatrix(M) return M
[docs]def from_numpy_matrix(A,create_using=None): """Return a graph from numpy matrix. The numpy matrix is interpreted as an adjacency matrix for the graph. Parameters ---------- A : numpy matrix An adjacency matrix representation of a graph create_using : NetworkX graph Use specified graph for result. The default is Graph() Notes ----- If the numpy matrix has a single data type for each matrix entry it will be converted to an appropriate Python data type. If the numpy matrix has a user-specified compound data type the names of the data fields will be used as attribute keys in the resulting NetworkX graph. See Also -------- to_numpy_matrix, to_numpy_recarray Examples -------- Simple integer weights on edges: >>> import numpy >>> A=numpy.matrix([[1,1],[2,1]]) >>> G=nx.from_numpy_matrix(A) User defined compound data type on edges: >>> import numpy >>> dt=[('weight',float),('cost',int)] >>> A=numpy.matrix([[(1.0,2)]],dtype=dt) >>> G=nx.from_numpy_matrix(A) >>> G.edges() [(0, 0)] >>> G[0][0]['cost'] 2 >>> G[0][0]['weight'] 1.0 """ # This should never fail if you have created a numpy matrix with numpy... import numpy as np kind_to_python_type={'f':float, 'i':int, 'u':int, 'b':bool, 'c':complex, 'S':str, 'V':'void'} try: # Python 3.x blurb = chr(1245) # just to trigger the exception kind_to_python_type['U']=str except ValueError: # Python 2.6+ kind_to_python_type['U']=unicode G=_prep_create_using(create_using) n,m=A.shape if n!=m: raise nx.NetworkXError("Adjacency matrix is not square.", "nx,ny=%s"%(A.shape,)) dt=A.dtype try: python_type=kind_to_python_type[dt.kind] except: raise TypeError("Unknown numpy data type: %s"%dt) # make sure we get isolated nodes G.add_nodes_from(range(n)) # get a list of edges x,y=np.asarray(A).nonzero() # handle numpy constructed data type if python_type is 'void': fields=sorted([(offset,dtype,name) for name,(dtype,offset) in A.dtype.fields.items()]) for (u,v) in zip(x,y): attr={} for (offset,dtype,name),val in zip(fields,A[u,v]): attr[name]=kind_to_python_type[dtype.kind](val) G.add_edge(u,v,attr) else: # basic data type G.add_edges_from( ((u,v,{'weight':python_type(A[u,v])}) for (u,v) in zip(x,y)) ) return G
@not_implemented_for('multigraph')
[docs]def to_numpy_recarray(G,nodelist=None, dtype=[('weight',float)], order=None): """Return the graph adjacency matrix as a NumPy recarray. Parameters ---------- G : graph The NetworkX graph used to construct the NumPy matrix. 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(). dtype : NumPy data-type, optional A valid NumPy named dtype used to initialize the NumPy recarray. The data type names are assumed to be keys in the graph edge attribute dictionary. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. If None, then the NumPy default is used. Returns ------- M : NumPy recarray The graph with specified edge data as a Numpy recarray Notes ----- When `nodelist` does not contain every node in `G`, the matrix is built from the subgraph of `G` that is induced by the nodes in `nodelist`. Examples -------- >>> G = nx.Graph() >>> G.add_edge(1,2,weight=7.0,cost=5) >>> A=nx.to_numpy_recarray(G,dtype=[('weight',float),('cost',int)]) >>> print(A.weight) [[ 0. 7.] [ 7. 0.]] >>> print(A.cost) [[0 5] [5 0]] """ import numpy as np if nodelist is None: nodelist = G.nodes() nodeset = set(nodelist) if len(nodelist) != len(nodeset): msg = "Ambiguous ordering: `nodelist` contained duplicates." raise nx.NetworkXError(msg) nlen=len(nodelist) undirected = not G.is_directed() index=dict(zip(nodelist,range(nlen))) M = np.zeros((nlen,nlen), dtype=dtype, order=order) names=M.dtype.names for u,v,attrs in G.edges_iter(data=True): if (u in nodeset) and (v in nodeset): i,j = index[u],index[v] values=tuple([attrs[n] for n in names]) M[i,j] = values if undirected: M[j,i] = M[i,j] return M.view(np.recarray)
[docs]def to_scipy_sparse_matrix(G, nodelist=None, dtype=None, weight='weight', format='csr'): """Return the graph adjacency matrix as a SciPy sparse matrix. Parameters ---------- G : graph The NetworkX graph used to construct the NumPy matrix. 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(). dtype : NumPy data-type, optional A valid NumPy dtype used to initialize the array. If None, then the NumPy default is used. weight : string or None optional (default='weight') The edge attribute that holds the numerical value used for the edge weight. If None then all edge weights are 1. format : str in {'bsr', 'csr', 'csc', 'coo', 'lil', 'dia', 'dok'} The type of the matrix to be returned (default 'csr'). For some algorithms different implementations of sparse matrices can perform better. See [1]_ for details. Returns ------- M : SciPy sparse matrix Graph adjacency matrix. Notes ----- The matrix entries are populated using the edge attribute held in parameter weight. When an edge does not have that attribute, the value of the entry is 1. For multiple edges the matrix values are the sums of the edge weights. When `nodelist` does not contain every node in `G`, the matrix is built from the subgraph of `G` that is induced by the nodes in `nodelist`. Uses coo_matrix format. To convert to other formats specify the format= keyword. The convention used for self-loop edges in graphs is to assign the diagonal matrix entry value to the weight attribute of the edge (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.to_scipy_sparse_matrix(G) >>> print(A.todense()) [[1]] >>> A.setdiag(A.diagonal()*2) >>> print(A.todense()) [[2]] Examples -------- >>> G = nx.MultiDiGraph() >>> G.add_edge(0,1,weight=2) >>> G.add_edge(1,0) >>> G.add_edge(2,2,weight=3) >>> G.add_edge(2,2) >>> S = nx.to_scipy_sparse_matrix(G, nodelist=[0,1,2]) >>> print(S.todense()) [[0 2 0] [1 0 0] [0 0 4]] References ---------- .. [1] Scipy Dev. References, "Sparse Matrices", http://docs.scipy.org/doc/scipy/reference/sparse.html """ from scipy import sparse if nodelist is None: nodelist = G nlen = len(nodelist) if nlen == 0: raise nx.NetworkXError("Graph has no nodes or edges") if len(nodelist) != len(set(nodelist)): msg = "Ambiguous ordering: `nodelist` contained duplicates." raise nx.NetworkXError(msg) index = dict(zip(nodelist,range(nlen))) if G.number_of_edges() == 0: row,col,data=[],[],[] else: row,col,data = zip(*((index[u],index[v],d.get(weight,1)) for u,v,d in G.edges_iter(nodelist, data=True) if u in index and v in index)) if G.is_directed(): M = sparse.coo_matrix((data,(row,col)), shape=(nlen,nlen), dtype=dtype) else: # symmetrize matrix d = data + data r = row + col c = col + row # selfloop entries get double counted when symmetrizing # so we subtract the data on the diagonal selfloops = G.selfloop_edges(data=True) if selfloops: diag_index,diag_data = zip(*((index[u],-d.get(weight,1)) for u,v,d in selfloops if u in index and v in index)) d += diag_data r += diag_index c += diag_index M = sparse.coo_matrix((d, (r, c)), shape=(nlen,nlen), dtype=dtype) try: return M.asformat(format) except AttributeError: raise nx.NetworkXError("Unknown sparse matrix format: %s"%format)
[docs]def from_scipy_sparse_matrix(A, create_using=None, edge_attribute='weight'): """Return a graph from scipy sparse matrix adjacency list. Parameters ---------- A: scipy sparse matrix An adjacency matrix representation of a graph create_using: NetworkX graph Use specified graph for result. The default is Graph() edge_attribute: string Name of edge attrbute to store matrix numeric value. The data will have the same type as the matrix entry (int, float, (real,imag)). Examples -------- >>> import scipy.sparse >>> A = scipy.sparse.eye(2,2,1) >>> G = nx.from_scipy_sparse_matrix(A) """ G = _prep_create_using(create_using) n,m = A.shape if n != m: raise nx.NetworkXError(\ "Adjacency matrix is not square. nx,ny=%s"%(A.shape,)) G.add_nodes_from(range(n)) # make sure we get isolated nodes if A.format == 'coo': for i,j,d in zip(A.row, A.col, A.data): G.add_edge(i,j,**{edge_attribute:d}) elif A.format == 'dia': # make a copy - could be done more efficiently B = A.tocoo() for i,j,d in zip(B.row, B.col, B.data): G.add_edge(i,j,**{edge_attribute:d}) else: for i,j in zip(*A.nonzero()): G.add_edge(i,j,**{edge_attribute:A[i,j]}) return G # fixture for nose tests
def setup_module(module): from nose import SkipTest try: import numpy except: raise SkipTest("NumPy not available") try: import scipy except: raise SkipTest("SciPy not available")