# Source code for networkx.algorithms.bipartite.basic

"""
==========================
Bipartite Graph Algorithms
==========================
"""
import networkx as nx
from networkx.algorithms.components import connected_components
from networkx.exception import AmbiguousSolution

__all__ = [
"is_bipartite",
"is_bipartite_node_set",
"color",
"sets",
"density",
"degrees",
]

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