# networkx.algorithms.bipartite.projection.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])
>>> list(G)
[1, 3]
>>> list(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 bipartite documentation for further details on how bipartite graphs are handled in NetworkX.