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# generic_weighted_projected_graph

generic_weighted_projected_graph(B, nodes, weight_function=None)

  Weighted projection of B with a user-specified weight function.

  The bipartite network B is projected on to the specified nodes with weights computed by a user-specified function. This function must accept as a parameter the neighborhood sets of two nodes and return an integer or a float.

  The nodes retain their attributes and are connected in the resulting graph if they have an edge to a common node in the original graph.

  Parameters:
    B NetworkX graph

      The input graph should be bipartite.

    nodes list or iterable

      Nodes to project onto (the “bottom” nodes).

    weight_function function

      This function must accept as parameters the same input graph that this function, and two nodes; and return an integer or a float. The default function computes the number of shared neighbors.

  Returns:
    Graph NetworkX graph

      A graph that is the projection onto the given nodes.

  See also

  `is_bipartite`
  `is_bipartite_node_set`
  `sets`
  `weighted_projected_graph`
  `collaboration_weighted_projected_graph`
  `overlap_weighted_projected_graph`
  `projected_graph`

  Notes

  No attempt is made to verify that the input graph B is bipartite. 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.

  Examples

      >>> from networkx.algorithms import bipartite
      >>> # Define some custom weight functions
      >>> def jaccard(G, u, v):
      ...     unbrs = set(G[u])
      ...     vnbrs = set(G[v])
      ...     return float(len(unbrs & vnbrs)) / len(unbrs | vnbrs)
      >>> def my_weight(G, u, v, weight="weight"):
      ...     w = 0
      ...     for nbr in set(G[u]) & set(G[v]):
      ...         w += G[u][nbr].get(weight, 1) + G[v][nbr].get(weight, 1)
      ...     return w
      >>> # A complete bipartite graph with 4 nodes and 4 edges
      >>> B = nx.complete_bipartite_graph(2, 2)
      >>> # Add some arbitrary weight to the edges
      >>> for i, (u, v) in enumerate(B.edges()):
      ...     B.edges[u, v]["weight"] = i + 1
      >>> for edge in B.edges(data=True):
      ...     print(edge)
      (0, 2, {'weight': 1})
      (0, 3, {'weight': 2})
      (1, 2, {'weight': 3})
      (1, 3, {'weight': 4})
      >>> # By default, the weight is the number of shared neighbors
      >>> G = bipartite.generic_weighted_projected_graph(B, [0, 1])
      >>> print(list(G.edges(data=True)))
      [(0, 1, {'weight': 2})]
      >>> # To specify a custom weight function use the weight_function parameter
      >>> G = bipartite.generic_weighted_projected_graph(
      ...     B, [0, 1], weight_function=jaccard
      ... )
      >>> print(list(G.edges(data=True)))
      [(0, 1, {'weight': 1.0})]
      >>> G = bipartite.generic_weighted_projected_graph(
      ...     B, [0, 1], weight_function=my_weight
      ... )
      >>> print(list(G.edges(data=True)))
      [(0, 1, {'weight': 10})]