Source code for networkx.convert_matrix

#    Copyright (C) 2006-2019 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
"""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 constructor.  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 as np
>>> a = np.random.randint(0, 2, size=(10, 10))
>>> D = nx.DiGraph(a)

or equivalently

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

See Also
--------
nx_agraph, nx_pydot
"""

import itertools
import networkx as nx
from networkx.utils import not_implemented_for

__all__ = ['from_numpy_matrix', 'to_numpy_matrix',
           'from_pandas_adjacency', 'to_pandas_adjacency',
           'from_pandas_edgelist', 'to_pandas_edgelist',
           'to_numpy_recarray',
           'from_scipy_sparse_matrix', 'to_scipy_sparse_matrix',
           'from_numpy_array', 'to_numpy_array']


[docs]def to_pandas_adjacency(G, nodelist=None, dtype=None, order=None, multigraph_weight=sum, weight='weight', nonedge=0.0): """Returns the graph adjacency matrix as a Pandas DataFrame. Parameters ---------- G : graph The NetworkX graph used to construct the Pandas DataFrame. 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(). 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 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, optional 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 ------- df : Pandas DataFrame Graph adjacency matrix Notes ----- For directed graphs, entry i,j corresponds to an edge from i to j. The DataFrame 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' parameter. 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 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 Pandas DataFrame can be modified as follows: >>> import pandas as pd >>> pd.options.display.max_columns = 20 >>> import numpy as np >>> G = nx.Graph([(1, 1)]) >>> df = nx.to_pandas_adjacency(G, dtype=int) >>> df 1 1 1 >>> df.values[np.diag_indices_from(df)] *= 2 >>> df 1 1 2 Examples -------- >>> G = nx.MultiDiGraph() >>> G.add_edge(0, 1, weight=2) 0 >>> G.add_edge(1, 0) 0 >>> G.add_edge(2, 2, weight=3) 0 >>> G.add_edge(2, 2) 1 >>> nx.to_pandas_adjacency(G, nodelist=[0, 1, 2], dtype=int) 0 1 2 0 0 2 0 1 1 0 0 2 0 0 4 """ import pandas as pd M = to_numpy_array(G, nodelist=nodelist, dtype=dtype, order=order, multigraph_weight=multigraph_weight, weight=weight, nonedge=nonedge) if nodelist is None: nodelist = list(G) return pd.DataFrame(data=M, index=nodelist, columns=nodelist)
[docs]def from_pandas_adjacency(df, create_using=None): r"""Returns a graph from Pandas DataFrame. The Pandas DataFrame is interpreted as an adjacency matrix for the graph. Parameters ---------- df : Pandas DataFrame An adjacency matrix representation of a graph create_using : NetworkX graph constructor, optional (default=nx.Graph) Graph type to create. If graph instance, then cleared before populated. Notes ----- For directed graphs, explicitly mention create_using=nx.Digraph, and entry i,j of df corresponds to an edge from i to j. 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_pandas_adjacency Examples -------- Simple integer weights on edges: >>> import pandas as pd >>> pd.options.display.max_columns = 20 >>> df = pd.DataFrame([[1, 1], [2, 1]]) >>> df 0 1 0 1 1 1 2 1 >>> G = nx.from_pandas_adjacency(df) >>> G.name = 'Graph from pandas adjacency matrix' >>> print(nx.info(G)) Name: Graph from pandas adjacency matrix Type: Graph Number of nodes: 2 Number of edges: 3 Average degree: 3.0000 """ try: df = df[df.index] except Exception: msg = "%s not in columns" missing = list(set(df.index).difference(set(df.columns))) raise nx.NetworkXError("Columns must match Indices.", msg % missing) A = df.values G = from_numpy_matrix(A, create_using=create_using) nx.relabel.relabel_nodes(G, dict(enumerate(df.columns)), copy=False) return G
[docs]def to_pandas_edgelist(G, source='source', target='target', nodelist=None, dtype=None, order=None): """Returns the graph edge list as a Pandas DataFrame. Parameters ---------- G : graph The NetworkX graph used to construct the Pandas DataFrame. source : str or int, optional A valid column name (string or integer) for the source nodes (for the directed case). target : str or int, optional A valid column name (string or integer) for the target nodes (for the directed case). nodelist : list, optional Use only nodes specified in nodelist Returns ------- df : Pandas DataFrame Graph edge list Examples -------- >>> G = nx.Graph([('A', 'B', {'cost': 1, 'weight': 7}), ... ('C', 'E', {'cost': 9, 'weight': 10})]) >>> df = nx.to_pandas_edgelist(G, nodelist=['A', 'C']) >>> df[['source', 'target', 'cost', 'weight']] source target cost weight 0 A B 1 7 1 C E 9 10 """ import pandas as pd if nodelist is None: edgelist = G.edges(data=True) else: edgelist = G.edges(nodelist, data=True) source_nodes = [s for s, t, d in edgelist] target_nodes = [t for s, t, d in edgelist] all_keys = set().union(*(d.keys() for s, t, d in edgelist)) edge_attr = {k: [d.get(k, float("nan")) for s, t, d in edgelist] for k in all_keys} edgelistdict = {source: source_nodes, target: target_nodes} edgelistdict.update(edge_attr) return pd.DataFrame(edgelistdict)
[docs]def from_pandas_edgelist(df, source='source', target='target', edge_attr=None, create_using=None): """Returns a graph from Pandas DataFrame containing an edge list. The Pandas DataFrame should contain at least two columns of node names and zero or more columns of edge attributes. Each row will be processed as one edge instance. Note: This function iterates over DataFrame.values, which is not guaranteed to retain the data type across columns in the row. This is only a problem if your row is entirely numeric and a mix of ints and floats. In that case, all values will be returned as floats. See the DataFrame.iterrows documentation for an example. Parameters ---------- df : Pandas DataFrame An edge list representation of a graph source : str or int A valid column name (string or integer) for the source nodes (for the directed case). target : str or int A valid column name (string or integer) for the target nodes (for the directed case). edge_attr : str or int, iterable, True, or None A valid column name (str or int) or iterable of column names that are used to retrieve items and add them to the graph as edge attributes. If `True`, all of the remaining columns will be added. If `None`, no edge attributes are added to the graph. create_using : NetworkX graph constructor, optional (default=nx.Graph) Graph type to create. If graph instance, then cleared before populated. See Also -------- to_pandas_edgelist Examples -------- Simple integer weights on edges: >>> import pandas as pd >>> pd.options.display.max_columns = 20 >>> import numpy as np >>> rng = np.random.RandomState(seed=5) >>> ints = rng.randint(1, 11, size=(3,2)) >>> a = ['A', 'B', 'C'] >>> b = ['D', 'A', 'E'] >>> df = pd.DataFrame(ints, columns=['weight', 'cost']) >>> df[0] = a >>> df['b'] = b >>> df[['weight', 'cost', 0, 'b']] weight cost 0 b 0 4 7 A D 1 7 1 B A 2 10 9 C E >>> G = nx.from_pandas_edgelist(df, 0, 'b', ['weight', 'cost']) >>> G['E']['C']['weight'] 10 >>> G['E']['C']['cost'] 9 >>> edges = pd.DataFrame({'source': [0, 1, 2], ... 'target': [2, 2, 3], ... 'weight': [3, 4, 5], ... 'color': ['red', 'blue', 'blue']}) >>> G = nx.from_pandas_edgelist(edges, edge_attr=True) >>> G[0][2]['color'] 'red' """ g = nx.empty_graph(0, create_using) if edge_attr is None: g.add_edges_from(zip(df[source], df[target])) return g # Additional columns requested if edge_attr is True: cols = [c for c in df.columns if c is not source and c is not target] elif isinstance(edge_attr, (list, tuple)): cols = edge_attr else: cols = [edge_attr] if len(cols) == 0: msg = "Invalid edge_attr argument. No columns found with name: %s" raise nx.NetworkXError(msg % cols) try: eattrs = zip(*[df[col] for col in cols]) except (KeyError, TypeError) as e: msg = "Invalid edge_attr argument: %s" % edge_attr raise nx.NetworkXError(msg) for s, t, attrs in zip(df[source], df[target], eattrs): if g.is_multigraph(): key = g.add_edge(s, t) g[s][t][key].update(zip(cols, attrs)) else: g.add_edge(s, t) g[s][t].update(zip(cols, attrs)) return g
[docs]def to_numpy_matrix(G, nodelist=None, dtype=None, order=None, multigraph_weight=sum, weight='weight', nonedge=0.0): """Returns 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 ----- For directed graphs, entry i,j corresponds to an edge from i to j. 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` parameter. 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 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 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[np.diag_indices_from(A)] *= 2 >>> A matrix([[2.]]) Examples -------- >>> G = nx.MultiDiGraph() >>> G.add_edge(0, 1, weight=2) 0 >>> G.add_edge(1, 0) 0 >>> G.add_edge(2, 2, weight=3) 0 >>> G.add_edge(2, 2) 1 >>> nx.to_numpy_matrix(G, nodelist=[0, 1, 2]) matrix([[0., 2., 0.], [1., 0., 0.], [0., 0., 4.]]) """ import numpy as np A = to_numpy_array(G, nodelist=nodelist, dtype=dtype, order=order, multigraph_weight=multigraph_weight, weight=weight, nonedge=nonedge) M = np.asmatrix(A, dtype=dtype) return M
[docs]def from_numpy_matrix(A, parallel_edges=False, create_using=None): """Returns 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 parallel_edges : Boolean If True, `create_using` is a multigraph, and `A` is an integer matrix, then entry *(i, j)* in the matrix is interpreted as the number of parallel edges joining vertices *i* and *j* in the graph. If False, then the entries in the adjacency matrix are interpreted as the weight of a single edge joining the vertices. create_using : NetworkX graph constructor, optional (default=nx.Graph) Graph type to create. If graph instance, then cleared before populated. Notes ----- For directed graphs, explicitly mention create_using=nx.Digraph, and entry i,j of A corresponds to an edge from i to j. If `create_using` is :class:`networkx.MultiGraph` or :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the entries of `A` are of type :class:`int`, then this function returns a multigraph (constructed from `create_using`) with parallel edges. If `create_using` indicates an undirected multigraph, then only the edges indicated by the upper triangle of the matrix `A` will be added to the graph. 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 as np >>> A = np.array([[1, 1], [2, 1]]) >>> G = nx.from_numpy_matrix(A) If `create_using` indicates a multigraph and the matrix has only integer entries and `parallel_edges` is False, then the entries will be treated as weights for edges joining the nodes (without creating parallel edges): >>> A = np.array([[1, 1], [1, 2]]) >>> G = nx.from_numpy_matrix(A, create_using=nx.MultiGraph) >>> G[1][1] AtlasView({0: {'weight': 2}}) If `create_using` indicates a multigraph and the matrix has only integer entries and `parallel_edges` is True, then the entries will be treated as the number of parallel edges joining those two vertices: >>> A = np.array([[1, 1], [1, 2]]) >>> temp = nx.MultiGraph() >>> G = nx.from_numpy_matrix(A, parallel_edges=True, create_using=temp) >>> G[1][1] AtlasView({0: {'weight': 1}, 1: {'weight': 1}}) User defined compound data type on edges: >>> dt = [('weight', float), ('cost', int)] >>> A = np.array([[(1.0, 2)]], dtype=dt) >>> G = nx.from_numpy_matrix(A) >>> list(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 2.7 kind_to_python_type['U'] = unicode G = nx.empty_graph(0, 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 Exception: raise TypeError("Unknown numpy data type: %s" % dt) # Make sure we get even the isolated nodes of the graph. G.add_nodes_from(range(n)) # Get a list of all the entries in the matrix with nonzero entries. These # coordinates will become the edges in the graph. edges = map(lambda e: (int(e[0]), int(e[1])), zip(*(np.asarray(A).nonzero()))) # handle numpy constructed data type if python_type == 'void': # Sort the fields by their offset, then by dtype, then by name. fields = sorted((offset, dtype, name) for name, (dtype, offset) in A.dtype.fields.items()) triples = ((u, v, {name: kind_to_python_type[dtype.kind](val) for (_, dtype, name), val in zip(fields, A[u, v])}) for u, v in edges) # If the entries in the adjacency matrix are integers, the graph is a # multigraph, and parallel_edges is True, then create parallel edges, each # with weight 1, for each entry in the adjacency matrix. Otherwise, create # one edge for each positive entry in the adjacency matrix and set the # weight of that edge to be the entry in the matrix. elif python_type is int and G.is_multigraph() and parallel_edges: chain = itertools.chain.from_iterable # The following line is equivalent to: # # for (u, v) in edges: # for d in range(A[u, v]): # G.add_edge(u, v, weight=1) # triples = chain(((u, v, dict(weight=1)) for d in range(A[u, v])) for (u, v) in edges) else: # basic data type triples = ((u, v, dict(weight=python_type(A[u, v]))) for u, v in edges) # If we are creating an undirected multigraph, only add the edges from the # upper triangle of the matrix. Otherwise, add all the edges. This relies # on the fact that the vertices created in the # `_generated_weighted_edges()` function are actually the row/column # indices for the matrix `A`. # # Without this check, we run into a problem where each edge is added twice # when `G.add_edges_from()` is invoked below. if G.is_multigraph() and not G.is_directed(): triples = ((u, v, d) for u, v, d in triples if u <= v) G.add_edges_from(triples) return G
[docs]@not_implemented_for('multigraph') def to_numpy_recarray(G, nodelist=None, dtype=None, order=None): """Returns 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]] """ if dtype is None: dtype = [('weight', float)] import numpy as np if nodelist is None: nodelist = list(G) 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(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'): """Returns 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 ----- For directed graphs, matrix entry i,j corresponds to an edge from i to j. 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) 0 >>> G.add_edge(1, 0) 0 >>> G.add_edge(2, 2, weight=3) 0 >>> G.add_edge(2, 2) 1 >>> 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", https://docs.scipy.org/doc/scipy/reference/sparse.html """ from scipy import sparse if nodelist is None: nodelist = list(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))) coefficients = zip(*((index[u], index[v], d.get(weight, 1)) for u, v, d in G.edges(nodelist, data=True) if u in index and v in index)) try: row, col, data = coefficients except ValueError: # there is no edge in the subgraph row, col, data = [], [], [] 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 = list(nx.selfloop_edges(G, 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) # From Scipy 1.1.0, asformat will throw a ValueError instead of an # AttributeError if the format if not recognized. except (AttributeError, ValueError): raise nx.NetworkXError("Unknown sparse matrix format: %s" % format)
def _csr_gen_triples(A): """Converts a SciPy sparse matrix in **Compressed Sparse Row** format to an iterable of weighted edge triples. """ nrows = A.shape[0] data, indices, indptr = A.data, A.indices, A.indptr for i in range(nrows): for j in range(indptr[i], indptr[i + 1]): yield i, indices[j], data[j] def _csc_gen_triples(A): """Converts a SciPy sparse matrix in **Compressed Sparse Column** format to an iterable of weighted edge triples. """ ncols = A.shape[1] data, indices, indptr = A.data, A.indices, A.indptr for i in range(ncols): for j in range(indptr[i], indptr[i + 1]): yield indices[j], i, data[j] def _coo_gen_triples(A): """Converts a SciPy sparse matrix in **Coordinate** format to an iterable of weighted edge triples. """ row, col, data = A.row, A.col, A.data return zip(row, col, data) def _dok_gen_triples(A): """Converts a SciPy sparse matrix in **Dictionary of Keys** format to an iterable of weighted edge triples. """ for (r, c), v in A.items(): yield r, c, v def _generate_weighted_edges(A): """Returns an iterable over (u, v, w) triples, where u and v are adjacent vertices and w is the weight of the edge joining u and v. `A` is a SciPy sparse matrix (in any format). """ if A.format == 'csr': return _csr_gen_triples(A) if A.format == 'csc': return _csc_gen_triples(A) if A.format == 'dok': return _dok_gen_triples(A) # If A is in any other format (including COO), convert it to COO format. return _coo_gen_triples(A.tocoo())
[docs]def from_scipy_sparse_matrix(A, parallel_edges=False, create_using=None, edge_attribute='weight'): """Creates a new graph from an adjacency matrix given as a SciPy sparse matrix. Parameters ---------- A: scipy sparse matrix An adjacency matrix representation of a graph parallel_edges : Boolean If this is True, `create_using` is a multigraph, and `A` is an integer matrix, then entry *(i, j)* in the matrix is interpreted as the number of parallel edges joining vertices *i* and *j* in the graph. If it is False, then the entries in the matrix are interpreted as the weight of a single edge joining the vertices. create_using : NetworkX graph constructor, optional (default=nx.Graph) Graph type to create. If graph instance, then cleared before populated. edge_attribute: string Name of edge attribute to store matrix numeric value. The data will have the same type as the matrix entry (int, float, (real,imag)). Notes ----- For directed graphs, explicitly mention create_using=nx.Digraph, and entry i,j of A corresponds to an edge from i to j. If `create_using` is :class:`networkx.MultiGraph` or :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the entries of `A` are of type :class:`int`, then this function returns a multigraph (constructed from `create_using`) with parallel edges. In this case, `edge_attribute` will be ignored. If `create_using` indicates an undirected multigraph, then only the edges indicated by the upper triangle of the matrix `A` will be added to the graph. Examples -------- >>> import scipy as sp >>> A = sp.sparse.eye(2, 2, 1) >>> G = nx.from_scipy_sparse_matrix(A) If `create_using` indicates a multigraph and the matrix has only integer entries and `parallel_edges` is False, then the entries will be treated as weights for edges joining the nodes (without creating parallel edges): >>> A = sp.sparse.csr_matrix([[1, 1], [1, 2]]) >>> G = nx.from_scipy_sparse_matrix(A, create_using=nx.MultiGraph) >>> G[1][1] AtlasView({0: {'weight': 2}}) If `create_using` indicates a multigraph and the matrix has only integer entries and `parallel_edges` is True, then the entries will be treated as the number of parallel edges joining those two vertices: >>> A = sp.sparse.csr_matrix([[1, 1], [1, 2]]) >>> G = nx.from_scipy_sparse_matrix(A, parallel_edges=True, ... create_using=nx.MultiGraph) >>> G[1][1] AtlasView({0: {'weight': 1}, 1: {'weight': 1}}) """ G = nx.empty_graph(0, create_using) n, m = A.shape if n != m: raise nx.NetworkXError( "Adjacency matrix is not square. nx,ny=%s" % (A.shape,)) # Make sure we get even the isolated nodes of the graph. G.add_nodes_from(range(n)) # Create an iterable over (u, v, w) triples and for each triple, add an # edge from u to v with weight w. triples = _generate_weighted_edges(A) # If the entries in the adjacency matrix are integers, the graph is a # multigraph, and parallel_edges is True, then create parallel edges, each # with weight 1, for each entry in the adjacency matrix. Otherwise, create # one edge for each positive entry in the adjacency matrix and set the # weight of that edge to be the entry in the matrix. if A.dtype.kind in ('i', 'u') and G.is_multigraph() and parallel_edges: chain = itertools.chain.from_iterable # The following line is equivalent to: # # for (u, v) in edges: # for d in range(A[u, v]): # G.add_edge(u, v, weight=1) # triples = chain(((u, v, 1) for d in range(w)) for (u, v, w) in triples) # If we are creating an undirected multigraph, only add the edges from the # upper triangle of the matrix. Otherwise, add all the edges. This relies # on the fact that the vertices created in the # `_generated_weighted_edges()` function are actually the row/column # indices for the matrix `A`. # # Without this check, we run into a problem where each edge is added twice # when `G.add_weighted_edges_from()` is invoked below. if G.is_multigraph() and not G.is_directed(): triples = ((u, v, d) for u, v, d in triples if u <= v) G.add_weighted_edges_from(triples, weight=edge_attribute) return G
[docs]def to_numpy_array(G, nodelist=None, dtype=None, order=None, multigraph_weight=sum, weight='weight', nonedge=0.0): """Returns the graph adjacency matrix as a NumPy array. Parameters ---------- G : graph The NetworkX graph used to construct the NumPy array. 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 array values corresponding to nonedges are typically set to zero. However, this could be undesirable if there are array 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 ------- A : NumPy ndarray Graph adjacency matrix See Also -------- from_numpy_array Notes ----- For directed graphs, entry i,j corresponds to an edge from i to j. Entries in the adjacency matrix 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` parameter. The default is to sum the weight attributes for each of the parallel edges. When `nodelist` does not contain every node in `G`, the adjacency 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 array 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 NumPy array can be modified as follows: >>> import numpy as np >>> G = nx.Graph([(1, 1)]) >>> A = nx.to_numpy_array(G) >>> A array([[1.]]) >>> A[np.diag_indices_from(A)] *= 2 >>> A array([[2.]]) Examples -------- >>> G = nx.MultiDiGraph() >>> G.add_edge(0, 1, weight=2) 0 >>> G.add_edge(1, 0) 0 >>> G.add_edge(2, 2, weight=3) 0 >>> G.add_edge(2, 2) 1 >>> nx.to_numpy_array(G, nodelist=[0, 1, 2]) array([[0., 2., 0.], [1., 0., 0.], [0., 0., 4.]]) """ import numpy as np if nodelist is None: nodelist = list(G) 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 array # 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 A = np.full((nlen, nlen), np.nan, order=order) # use numpy nan-aware operations operator = {sum: np.nansum, min: np.nanmin, max: np.nanmax} try: op = operator[multigraph_weight] except Exception: raise ValueError('multigraph_weight must be sum, min, or max') for u, v, attrs in G.edges(data=True): if (u in nodeset) and (v in nodeset): i, j = index[u], index[v] e_weight = attrs.get(weight, 1) A[i, j] = op([e_weight, A[i, j]]) if undirected: A[j, i] = A[i, j] else: # Graph or DiGraph, this is much faster than above A = np.full((nlen, nlen), np.nan, order=order) for u, nbrdict in G.adjacency(): for v, d in nbrdict.items(): try: A[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 A[np.isnan(A)] = nonedge A = np.asarray(A, dtype=dtype) return A
[docs]def from_numpy_array(A, parallel_edges=False, create_using=None): """Returns a graph from NumPy array. The NumPy array is interpreted as an adjacency matrix for the graph. Parameters ---------- A : NumPy ndarray An adjacency matrix representation of a graph parallel_edges : Boolean If this is True, `create_using` is a multigraph, and `A` is an integer array, then entry *(i, j)* in the array is interpreted as the number of parallel edges joining vertices *i* and *j* in the graph. If it is False, then the entries in the array are interpreted as the weight of a single edge joining the vertices. create_using : NetworkX graph constructor, optional (default=nx.Graph) Graph type to create. If graph instance, then cleared before populated. Notes ----- For directed graphs, explicitly mention create_using=nx.Digraph, and entry i,j of A corresponds to an edge from i to j. If `create_using` is :class:`networkx.MultiGraph` or :class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the entries of `A` are of type :class:`int`, then this function returns a multigraph (of the same type as `create_using`) with parallel edges. If `create_using` indicates an undirected multigraph, then only the edges indicated by the upper triangle of the array `A` will be added to the graph. If the NumPy array has a single data type for each array entry it will be converted to an appropriate Python data type. If the NumPy array 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_array Examples -------- Simple integer weights on edges: >>> import numpy as np >>> A = np.array([[1, 1], [2, 1]]) >>> G = nx.from_numpy_array(A) >>> G.edges(data=True) EdgeDataView([(0, 0, {'weight': 1}), (0, 1, {'weight': 2}), \ (1, 1, {'weight': 1})]) If `create_using` indicates a multigraph and the array has only integer entries and `parallel_edges` is False, then the entries will be treated as weights for edges joining the nodes (without creating parallel edges): >>> A = np.array([[1, 1], [1, 2]]) >>> G = nx.from_numpy_array(A, create_using=nx.MultiGraph) >>> G[1][1] AtlasView({0: {'weight': 2}}) If `create_using` indicates a multigraph and the array has only integer entries and `parallel_edges` is True, then the entries will be treated as the number of parallel edges joining those two vertices: >>> A = np.array([[1, 1], [1, 2]]) >>> temp = nx.MultiGraph() >>> G = nx.from_numpy_array(A, parallel_edges=True, create_using=temp) >>> G[1][1] AtlasView({0: {'weight': 1}, 1: {'weight': 1}}) User defined compound data type on edges: >>> dt = [('weight', float), ('cost', int)] >>> A = np.array([[(1.0, 2)]], dtype=dt) >>> G = nx.from_numpy_array(A) >>> G.edges() EdgeView([(0, 0)]) >>> G[0][0]['cost'] 2 >>> G[0][0]['weight'] 1.0 """ return from_numpy_matrix(A, parallel_edges=parallel_edges, create_using=create_using)
# fixture for pytest def setup_module(module): import pytest numpy = pytest.importorskip('numpy') scipy = pytest.importorskip('scipy') pandas = pytest.importorskip('pandas')