1250 lines
44 KiB
Python
1250 lines
44 KiB
Python
# Copyright (C) 2006-2019 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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# All rights reserved.
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# BSD license.
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"""Functions to convert NetworkX graphs to and from numpy/scipy matrices.
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The preferred way of converting data to a NetworkX graph is through the
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graph constructor. The constructor calls the to_networkx_graph() function
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which attempts to guess the input type and convert it automatically.
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Examples
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--------
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Create a 10 node random graph from a numpy matrix
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>>> import numpy as np
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>>> a = np.random.randint(0, 2, size=(10, 10))
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>>> D = nx.DiGraph(a)
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or equivalently
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>>> D = nx.to_networkx_graph(a, create_using=nx.DiGraph)
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See Also
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--------
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nx_agraph, nx_pydot
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"""
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import itertools
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import networkx as nx
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from networkx.utils import not_implemented_for
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__all__ = ['from_numpy_matrix', 'to_numpy_matrix',
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'from_pandas_adjacency', 'to_pandas_adjacency',
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'from_pandas_edgelist', 'to_pandas_edgelist',
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'to_numpy_recarray',
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'from_scipy_sparse_matrix', 'to_scipy_sparse_matrix',
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'from_numpy_array', 'to_numpy_array']
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def to_pandas_adjacency(G, nodelist=None, dtype=None, order=None,
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multigraph_weight=sum, weight='weight', nonedge=0.0):
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"""Returns the graph adjacency matrix as a Pandas DataFrame.
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Parameters
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----------
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G : graph
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The NetworkX graph used to construct the Pandas DataFrame.
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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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multigraph_weight : {sum, min, max}, optional
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An operator that determines how weights in multigraphs are handled.
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The default is to sum the weights of the multiple edges.
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weight : string or None, optional
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The edge attribute that holds the numerical value used for
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the edge weight. If an edge does not have that attribute, then the
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value 1 is used instead.
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nonedge : float, optional
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The matrix values corresponding to nonedges are typically set to zero.
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However, this could be undesirable if there are matrix values
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corresponding to actual edges that also have the value zero. If so,
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one might prefer nonedges to have some other value, such as nan.
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Returns
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-------
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df : Pandas DataFrame
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Graph adjacency matrix
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Notes
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-----
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For directed graphs, entry i,j corresponds to an edge from i to j.
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The DataFrame entries are assigned to the weight edge attribute. When
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an edge does not have a weight attribute, the value of the entry is set to
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the number 1. For multiple (parallel) edges, the values of the entries
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are determined by the 'multigraph_weight' parameter. The default is to
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sum the weight attributes for each of the parallel edges.
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When `nodelist` does not contain every node in `G`, the matrix is built
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from the subgraph of `G` that is induced by the nodes in `nodelist`.
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The convention used for self-loop edges in graphs is to assign the
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diagonal matrix entry value to the weight attribute of the edge
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(or the number 1 if the edge has no weight attribute). If the
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alternate convention of doubling the edge weight is desired the
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resulting Pandas DataFrame can be modified as follows:
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>>> import pandas as pd
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>>> pd.options.display.max_columns = 20
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>>> import numpy as np
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>>> G = nx.Graph([(1, 1)])
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>>> df = nx.to_pandas_adjacency(G, dtype=int)
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>>> df
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1
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1 1
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>>> df.values[np.diag_indices_from(df)] *= 2
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>>> df
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1
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1 2
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Examples
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--------
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>>> G = nx.MultiDiGraph()
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>>> G.add_edge(0, 1, weight=2)
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0
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>>> G.add_edge(1, 0)
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0
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>>> G.add_edge(2, 2, weight=3)
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0
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>>> G.add_edge(2, 2)
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1
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>>> nx.to_pandas_adjacency(G, nodelist=[0, 1, 2], dtype=int)
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0 1 2
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0 0 2 0
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1 1 0 0
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2 0 0 4
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"""
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import pandas as pd
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M = to_numpy_array(G, nodelist=nodelist, dtype=dtype, order=order,
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multigraph_weight=multigraph_weight, weight=weight,
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nonedge=nonedge)
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if nodelist is None:
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nodelist = list(G)
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return pd.DataFrame(data=M, index=nodelist, columns=nodelist)
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def from_pandas_adjacency(df, create_using=None):
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r"""Returns a graph from Pandas DataFrame.
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The Pandas DataFrame is interpreted as an adjacency matrix for the graph.
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Parameters
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----------
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df : Pandas DataFrame
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An adjacency matrix representation of a graph
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create_using : NetworkX graph constructor, optional (default=nx.Graph)
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Graph type to create. If graph instance, then cleared before populated.
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Notes
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-----
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For directed graphs, explicitly mention create_using=nx.Digraph,
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and entry i,j of df corresponds to an edge from i to j.
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If the numpy matrix has a single data type for each matrix entry it
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will be converted to an appropriate Python data type.
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If the numpy matrix has a user-specified compound data type the names
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of the data fields will be used as attribute keys in the resulting
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NetworkX graph.
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See Also
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--------
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to_pandas_adjacency
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Examples
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--------
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Simple integer weights on edges:
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>>> import pandas as pd
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>>> pd.options.display.max_columns = 20
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>>> df = pd.DataFrame([[1, 1], [2, 1]])
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>>> df
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0 1
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0 1 1
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1 2 1
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>>> G = nx.from_pandas_adjacency(df)
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>>> G.name = 'Graph from pandas adjacency matrix'
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>>> print(nx.info(G))
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Name: Graph from pandas adjacency matrix
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Type: Graph
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Number of nodes: 2
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Number of edges: 3
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Average degree: 3.0000
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"""
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try:
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df = df[df.index]
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except Exception:
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msg = "%s not in columns"
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missing = list(set(df.index).difference(set(df.columns)))
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raise nx.NetworkXError("Columns must match Indices.", msg % missing)
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A = df.values
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G = from_numpy_matrix(A, create_using=create_using)
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nx.relabel.relabel_nodes(G, dict(enumerate(df.columns)), copy=False)
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return G
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def to_pandas_edgelist(G, source='source', target='target', nodelist=None,
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dtype=None, order=None):
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"""Returns the graph edge list as a Pandas DataFrame.
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Parameters
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----------
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G : graph
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The NetworkX graph used to construct the Pandas DataFrame.
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source : str or int, optional
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A valid column name (string or integer) for the source nodes (for the
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directed case).
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target : str or int, optional
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A valid column name (string or integer) for the target nodes (for the
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directed case).
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nodelist : list, optional
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Use only nodes specified in nodelist
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Returns
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-------
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df : Pandas DataFrame
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Graph edge list
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Examples
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--------
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>>> G = nx.Graph([('A', 'B', {'cost': 1, 'weight': 7}),
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... ('C', 'E', {'cost': 9, 'weight': 10})])
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>>> df = nx.to_pandas_edgelist(G, nodelist=['A', 'C'])
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>>> df[['source', 'target', 'cost', 'weight']]
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source target cost weight
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0 A B 1 7
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1 C E 9 10
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"""
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import pandas as pd
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if nodelist is None:
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edgelist = G.edges(data=True)
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else:
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edgelist = G.edges(nodelist, data=True)
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source_nodes = [s for s, t, d in edgelist]
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target_nodes = [t for s, t, d in edgelist]
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all_keys = set().union(*(d.keys() for s, t, d in edgelist))
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edge_attr = {k: [d.get(k, float("nan")) for s, t, d in edgelist]
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for k in all_keys}
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edgelistdict = {source: source_nodes, target: target_nodes}
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edgelistdict.update(edge_attr)
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return pd.DataFrame(edgelistdict)
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def from_pandas_edgelist(df, source='source', target='target', edge_attr=None,
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create_using=None):
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"""Returns a graph from Pandas DataFrame containing an edge list.
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The Pandas DataFrame should contain at least two columns of node names and
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zero or more columns of edge attributes. Each row will be processed as one
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edge instance.
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Note: This function iterates over DataFrame.values, which is not
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guaranteed to retain the data type across columns in the row. This is only
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a problem if your row is entirely numeric and a mix of ints and floats. In
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that case, all values will be returned as floats. See the
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DataFrame.iterrows documentation for an example.
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Parameters
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----------
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df : Pandas DataFrame
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An edge list representation of a graph
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source : str or int
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A valid column name (string or integer) for the source nodes (for the
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directed case).
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target : str or int
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A valid column name (string or integer) for the target nodes (for the
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directed case).
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edge_attr : str or int, iterable, True, or None
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A valid column name (str or int) or iterable of column names that are
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used to retrieve items and add them to the graph as edge attributes.
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If `True`, all of the remaining columns will be added.
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If `None`, no edge attributes are added to the graph.
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create_using : NetworkX graph constructor, optional (default=nx.Graph)
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Graph type to create. If graph instance, then cleared before populated.
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See Also
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--------
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to_pandas_edgelist
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Examples
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--------
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Simple integer weights on edges:
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>>> import pandas as pd
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>>> pd.options.display.max_columns = 20
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>>> import numpy as np
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>>> rng = np.random.RandomState(seed=5)
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>>> ints = rng.randint(1, 11, size=(3,2))
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>>> a = ['A', 'B', 'C']
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>>> b = ['D', 'A', 'E']
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>>> df = pd.DataFrame(ints, columns=['weight', 'cost'])
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>>> df[0] = a
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>>> df['b'] = b
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>>> df[['weight', 'cost', 0, 'b']]
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weight cost 0 b
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0 4 7 A D
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1 7 1 B A
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2 10 9 C E
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>>> G = nx.from_pandas_edgelist(df, 0, 'b', ['weight', 'cost'])
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>>> G['E']['C']['weight']
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10
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>>> G['E']['C']['cost']
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9
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>>> edges = pd.DataFrame({'source': [0, 1, 2],
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... 'target': [2, 2, 3],
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... 'weight': [3, 4, 5],
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... 'color': ['red', 'blue', 'blue']})
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>>> G = nx.from_pandas_edgelist(edges, edge_attr=True)
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>>> G[0][2]['color']
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'red'
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"""
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g = nx.empty_graph(0, create_using)
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if edge_attr is None:
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g.add_edges_from(zip(df[source], df[target]))
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return g
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# Additional columns requested
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if edge_attr is True:
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cols = [c for c in df.columns if c is not source and c is not target]
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elif isinstance(edge_attr, (list, tuple)):
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cols = edge_attr
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else:
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cols = [edge_attr]
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if len(cols) == 0:
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msg = "Invalid edge_attr argument. No columns found with name: %s"
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raise nx.NetworkXError(msg % cols)
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try:
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eattrs = zip(*[df[col] for col in cols])
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except (KeyError, TypeError) as e:
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msg = "Invalid edge_attr argument: %s" % edge_attr
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raise nx.NetworkXError(msg)
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for s, t, attrs in zip(df[source], df[target], eattrs):
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if g.is_multigraph():
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key = g.add_edge(s, t)
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g[s][t][key].update(zip(cols, attrs))
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else:
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g.add_edge(s, t)
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g[s][t].update(zip(cols, attrs))
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return g
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def to_numpy_matrix(G, nodelist=None, dtype=None, order=None,
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multigraph_weight=sum, weight='weight', nonedge=0.0):
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"""Returns the graph adjacency matrix as a NumPy matrix.
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Parameters
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----------
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G : graph
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The NetworkX graph used to construct the NumPy matrix.
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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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dtype : NumPy data type, optional
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A valid single NumPy data type used to initialize the array.
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This must be a simple type such as int or numpy.float64 and
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not a compound data type (see to_numpy_recarray)
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If None, then the NumPy default is used.
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order : {'C', 'F'}, optional
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Whether to store multidimensional data in C- or Fortran-contiguous
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(row- or column-wise) order in memory. If None, then the NumPy default
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is used.
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multigraph_weight : {sum, min, max}, optional
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An operator that determines how weights in multigraphs are handled.
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The default is to sum the weights of the multiple edges.
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weight : string or None optional (default = 'weight')
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The edge attribute that holds the numerical value used for
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the edge weight. If an edge does not have that attribute, then the
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value 1 is used instead.
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nonedge : float (default = 0.0)
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The matrix values corresponding to nonedges are typically set to zero.
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However, this could be undesirable if there are matrix values
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corresponding to actual edges that also have the value zero. If so,
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|
one might prefer nonedges to have some other value, such as nan.
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Returns
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-------
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M : NumPy matrix
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Graph adjacency matrix
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See Also
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--------
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to_numpy_recarray, from_numpy_matrix
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Notes
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-----
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For directed graphs, entry i,j corresponds to an edge from i to j.
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|
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The matrix entries are assigned to the weight edge attribute. When
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an edge does not have a weight attribute, the value of the entry is set to
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the number 1. For multiple (parallel) edges, the values of the entries
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|
are determined by the `multigraph_weight` parameter. The default is to
|
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sum the weight attributes for each of the parallel edges.
|
|
|
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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
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>>> G = nx.Graph([(1, 1)])
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>>> A = nx.to_numpy_matrix(G)
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>>> A
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matrix([[1.]])
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>>> A[np.diag_indices_from(A)] *= 2
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>>> A
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matrix([[2.]])
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Examples
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--------
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>>> G = nx.MultiDiGraph()
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>>> G.add_edge(0, 1, weight=2)
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0
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>>> G.add_edge(1, 0)
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0
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>>> G.add_edge(2, 2, weight=3)
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0
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>>> G.add_edge(2, 2)
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1
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>>> nx.to_numpy_matrix(G, nodelist=[0, 1, 2])
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matrix([[0., 2., 0.],
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[1., 0., 0.],
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[0., 0., 4.]])
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"""
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import numpy as np
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A = to_numpy_array(G, nodelist=nodelist, dtype=dtype, order=order,
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multigraph_weight=multigraph_weight, weight=weight,
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nonedge=nonedge)
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M = np.asmatrix(A, dtype=dtype)
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return M
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def from_numpy_matrix(A, parallel_edges=False, create_using=None):
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"""Returns a graph from numpy matrix.
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The numpy matrix is interpreted as an adjacency matrix for the graph.
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Parameters
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----------
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A : numpy matrix
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An adjacency matrix representation of a graph
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parallel_edges : Boolean
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If True, `create_using` is a multigraph, and `A` is an
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integer matrix, then entry *(i, j)* in the matrix is interpreted as the
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number of parallel edges joining vertices *i* and *j* in the graph.
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If False, then the entries in the adjacency matrix are interpreted as
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the weight of a single edge joining the vertices.
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create_using : NetworkX graph constructor, optional (default=nx.Graph)
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Graph type to create. If graph instance, then cleared before populated.
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|
Notes
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-----
|
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For directed graphs, explicitly mention create_using=nx.Digraph,
|
|
and entry i,j of A corresponds to an edge from i to j.
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|
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If `create_using` is :class:`networkx.MultiGraph` or
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:class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the
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entries of `A` are of type :class:`int`, then this function returns a
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multigraph (constructed from `create_using`) with parallel edges.
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If `create_using` indicates an undirected multigraph, then only the edges
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indicated by the upper triangle of the matrix `A` will be added to the
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graph.
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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
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|
--------
|
|
Simple integer weights on edges:
|
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|
|
>>> import numpy as np
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>>> A = np.array([[1, 1], [2, 1]])
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>>> G = nx.from_numpy_matrix(A)
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If `create_using` indicates a multigraph and the matrix has only integer
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entries and `parallel_edges` is False, then the entries will be treated
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as weights for edges joining the nodes (without creating parallel edges):
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>>> A = np.array([[1, 1], [1, 2]])
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>>> G = nx.from_numpy_matrix(A, create_using=nx.MultiGraph)
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>>> G[1][1]
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AtlasView({0: {'weight': 2}})
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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
|
|
|
|
|
|
@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)
|
|
|
|
|
|
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())
|
|
|
|
|
|
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
|
|
|
|
|
|
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
|
|
|
|
|
|
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')
|