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# common_neighbor_centrality

common_neighbor_centrality(G, ebunch=None, alpha=0.8)

  Return the CCPA score for each pair of nodes.

  Compute the Common Neighbor and Centrality based Parameterized Algorithm(CCPA) score of all node pairs in ebunch.

  CCPA score of `u` and `v` is defined as

  \[\alpha \cdot (|\Gamma (u){\cap }^{}\Gamma (v)|)+(1-\alpha )\cdot \frac{N}{{d}_{uv}}\]

  where \(\Gamma(u)\) denotes the set of neighbors of \(u\), \(\Gamma(v)\) denotes the set of neighbors of \(v\), \(\alpha\) is parameter varies between [0,1], \(N\) denotes total number of nodes in the Graph and \({d}_{uv}\) denotes shortest distance between \(u\) and \(v\).

  This algorithm is based on two vital properties of nodes, namely the number of common neighbors and their centrality. Common neighbor refers to the common nodes between two nodes. Centrality refers to the prestige that a node enjoys in a network.

  See also

  `common_neighbors()`

  Parameters:
    G graph

      NetworkX undirected graph.

    ebunch iterable of node pairs, optional (default = None)

      Preferential attachment score will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all nonexistent edges in the graph will be used. Default value: None.

    alpha Parameter defined for participation of Common Neighbor

      and Centrality Algorithm share. Values for alpha should normally be between 0 and 1. Default value set to 0.8 because author found better performance at 0.8 for all the dataset. Default value: 0.8

  Returns:
    piter iterator

      An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their Common Neighbor and Centrality based Parameterized Algorithm(CCPA) score.

  Raises:
    NetworkXNotImplemented

      If `G` is a `DiGraph`, a `Multigraph` or a `MultiDiGraph`.

    NetworkXAlgorithmError

      If self loops exist in `ebunch` or in `G` (if `ebunch` is `None`).

    NodeNotFound

      If `ebunch` has a node that is not in `G`.

  References

  [1]

  Ahmad, I., Akhtar, M.U., Noor, S. et al. Missing Link Prediction using Common Neighbor and Centrality based Parameterized Algorithm. Sci Rep 10, 364 (2020). https://doi.org/10.1038/s41598-019-57304-y

  Examples

      >>> G = nx.complete_graph(5)
      >>> preds = nx.common_neighbor_centrality(G, [(0, 1), (2, 3)])
      >>> for u, v, p in preds:
      ...     print(f"({u}, {v}) -> {p}")
      (0, 1) -> 3.4000000000000004
      (2, 3) -> 3.4000000000000004