308 lines
7.9 KiB
Python
308 lines
7.9 KiB
Python
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# -*- coding: utf-8 -*-
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"""
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==========================
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Bipartite Graph Algorithms
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==========================
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"""
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# Copyright (C) 2013-2019 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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import networkx as nx
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from networkx.algorithms.components import connected_components
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__author__ = """\n""".join(['Jordi Torrents <jtorrents@milnou.net>',
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'Aric Hagberg <aric.hagberg@gmail.com>'])
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__all__ = ['is_bipartite',
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'is_bipartite_node_set',
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'color',
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'sets',
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'density',
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'degrees']
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def color(G):
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"""Returns a two-coloring of the graph.
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Raises an exception if the graph is not bipartite.
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Parameters
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----------
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G : NetworkX graph
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Returns
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-------
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color : dictionary
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A dictionary keyed by node with a 1 or 0 as data for each node color.
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Raises
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------
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exc:`NetworkXError` if the graph is not two-colorable.
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Examples
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--------
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>>> from networkx.algorithms import bipartite
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>>> G = nx.path_graph(4)
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>>> c = bipartite.color(G)
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>>> print(c)
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{0: 1, 1: 0, 2: 1, 3: 0}
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You can use this to set a node attribute indicating the biparite set:
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>>> nx.set_node_attributes(G, c, 'bipartite')
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>>> print(G.nodes[0]['bipartite'])
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1
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>>> print(G.nodes[1]['bipartite'])
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0
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"""
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if G.is_directed():
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import itertools
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def neighbors(v):
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return itertools.chain.from_iterable([G.predecessors(v),
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G.successors(v)])
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else:
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neighbors = G.neighbors
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color = {}
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for n in G: # handle disconnected graphs
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if n in color or len(G[n]) == 0: # skip isolates
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continue
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queue = [n]
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color[n] = 1 # nodes seen with color (1 or 0)
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while queue:
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v = queue.pop()
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c = 1 - color[v] # opposite color of node v
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for w in neighbors(v):
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if w in color:
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if color[w] == color[v]:
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raise nx.NetworkXError("Graph is not bipartite.")
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else:
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color[w] = c
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queue.append(w)
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# color isolates with 0
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color.update(dict.fromkeys(nx.isolates(G), 0))
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return color
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def is_bipartite(G):
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""" Returns True if graph G is bipartite, False if not.
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Parameters
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----------
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G : NetworkX graph
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Examples
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--------
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>>> from networkx.algorithms import bipartite
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>>> G = nx.path_graph(4)
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>>> print(bipartite.is_bipartite(G))
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True
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See Also
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--------
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color, is_bipartite_node_set
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"""
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try:
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color(G)
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return True
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except nx.NetworkXError:
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return False
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def is_bipartite_node_set(G, nodes):
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"""Returns True if nodes and G/nodes are a bipartition of G.
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Parameters
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----------
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G : NetworkX graph
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nodes: list or container
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Check if nodes are a one of a bipartite set.
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Examples
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--------
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>>> from networkx.algorithms import bipartite
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>>> G = nx.path_graph(4)
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>>> X = set([1,3])
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>>> bipartite.is_bipartite_node_set(G,X)
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True
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Notes
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-----
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For connected graphs the bipartite sets are unique. This function handles
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disconnected graphs.
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"""
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S = set(nodes)
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for CC in (G.subgraph(c).copy() for c in connected_components(G)):
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X, Y = sets(CC)
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if not ((X.issubset(S) and Y.isdisjoint(S)) or
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(Y.issubset(S) and X.isdisjoint(S))):
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return False
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return True
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def sets(G, top_nodes=None):
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"""Returns bipartite node sets of graph G.
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Raises an exception if the graph is not bipartite or if the input
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graph is disconnected and thus more than one valid solution exists.
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See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
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for further details on how bipartite graphs are handled in NetworkX.
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Parameters
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----------
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G : NetworkX graph
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top_nodes : container, optional
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Container with all nodes in one bipartite node set. If not supplied
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it will be computed. But if more than one solution exists an exception
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will be raised.
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Returns
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-------
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X : set
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Nodes from one side of the bipartite graph.
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Y : set
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Nodes from the other side.
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Raises
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------
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AmbiguousSolution
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Raised if the input bipartite graph is disconnected and no container
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with all nodes in one bipartite set is provided. When determining
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the nodes in each bipartite set more than one valid solution is
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possible if the input graph is disconnected.
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NetworkXError
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Raised if the input graph is not bipartite.
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Examples
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--------
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>>> from networkx.algorithms import bipartite
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>>> G = nx.path_graph(4)
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>>> X, Y = bipartite.sets(G)
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>>> list(X)
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[0, 2]
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>>> list(Y)
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[1, 3]
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See Also
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--------
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color
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"""
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if G.is_directed():
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is_connected = nx.is_weakly_connected
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else:
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is_connected = nx.is_connected
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if top_nodes is not None:
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X = set(top_nodes)
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Y = set(G) - X
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else:
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if not is_connected(G):
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msg = 'Disconnected graph: Ambiguous solution for bipartite sets.'
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raise nx.AmbiguousSolution(msg)
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c = color(G)
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X = {n for n, is_top in c.items() if is_top}
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Y = {n for n, is_top in c.items() if not is_top}
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return (X, Y)
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def density(B, nodes):
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"""Returns density of bipartite graph B.
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Parameters
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----------
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G : NetworkX graph
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nodes: list or container
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Nodes in one node set of the bipartite graph.
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Returns
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-------
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d : float
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The bipartite density
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Examples
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--------
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>>> from networkx.algorithms import bipartite
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>>> G = nx.complete_bipartite_graph(3,2)
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>>> X=set([0,1,2])
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>>> bipartite.density(G,X)
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1.0
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>>> Y=set([3,4])
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>>> bipartite.density(G,Y)
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1.0
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Notes
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-----
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The container of nodes passed as argument must contain all nodes
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in one of the two bipartite node sets to avoid ambiguity in the
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case of disconnected graphs.
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See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
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for further details on how bipartite graphs are handled in NetworkX.
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See Also
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--------
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color
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"""
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n = len(B)
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m = nx.number_of_edges(B)
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nb = len(nodes)
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nt = n - nb
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if m == 0: # includes cases n==0 and n==1
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d = 0.0
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else:
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if B.is_directed():
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d = m / (2.0 * float(nb * nt))
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else:
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d = m / float(nb * nt)
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return d
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def degrees(B, nodes, weight=None):
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"""Returns the degrees of the two node sets in the bipartite graph B.
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Parameters
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----------
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G : NetworkX graph
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nodes: list or container
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Nodes in one node set of the bipartite graph.
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weight : string or None, optional (default=None)
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The edge attribute that holds the numerical value used as a weight.
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If None, then each edge has weight 1.
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The degree is the sum of the edge weights adjacent to the node.
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Returns
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-------
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(degX,degY) : tuple of dictionaries
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The degrees of the two bipartite sets as dictionaries keyed by node.
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Examples
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--------
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>>> from networkx.algorithms import bipartite
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>>> G = nx.complete_bipartite_graph(3,2)
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>>> Y=set([3,4])
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>>> degX,degY=bipartite.degrees(G,Y)
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>>> dict(degX)
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{0: 2, 1: 2, 2: 2}
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Notes
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-----
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The container of nodes passed as argument must contain all nodes
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in one of the two bipartite node sets to avoid ambiguity in the
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case of disconnected graphs.
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See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
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for further details on how bipartite graphs are handled in NetworkX.
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See Also
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--------
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color, density
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"""
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bottom = set(nodes)
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top = set(B) - bottom
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return (B.degree(top, weight), B.degree(bottom, weight))
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