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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 : NetworkX graph or multigraph

A graph that is the projection onto the given nodes.


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.


>>> 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']]