projected_graph¶

projected_graph
(B, nodes, multigraph=False)[source]¶ Returns the projection of B onto one of its node sets.
Returns the graph G that is the projection of the bipartite graph B onto the specified nodes. They retain their attributes and are connected in G if they have a common neighbor in B.
Parameters:  B (NetworkX graph) – The input graph should be bipartite.
 nodes (list or iterable) – Nodes to project onto (the “bottom” nodes).
 multigraph (bool (default=False)) – If True return a multigraph where the multiple edges represent multiple shared neighbors. They edge key in the multigraph is assigned to the label of the neighbor.
Returns: Graph – A graph that is the projection onto the given nodes.
Return type: NetworkX graph or multigraph
Examples
>>> from networkx.algorithms import bipartite >>> B = nx.path_graph(4) >>> G = bipartite.projected_graph(B, [1,3]) >>> print(G.nodes()) [1, 3] >>> print(G.edges()) [(1, 3)]
If nodes \(a\), and \(b\) are connected through both nodes 1 and 2 then building a multigraph results in two edges in the projection onto [\(a\),`b`]:
>>> B = nx.Graph() >>> B.add_edges_from([('a', 1), ('b', 1), ('a', 2), ('b', 2)]) >>> G = bipartite.projected_graph(B, ['a', 'b'], multigraph=True) >>> print([sorted((u,v)) for u,v in G.edges()]) [['a', 'b'], ['a', 'b']]
Notes
No attempt is made to verify that the input graph B is bipartite. Returns a simple graph that is the projection of the bipartite graph B onto the set of nodes given in list nodes. If multigraph=True then a multigraph is returned with an edge for every shared neighbor.
Directed graphs are allowed as input. The output will also then be a directed graph with edges if there is a directed path between the nodes.
The graph and node properties are (shallow) copied to the projected graph.
See also
is_bipartite()
,is_bipartite_node_set()
,sets()
,weighted_projected_graph()
,collaboration_weighted_projected_graph()
,overlap_weighted_projected_graph()
,generic_weighted_projected_graph()