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adamic_adar_index(G, ebunch=None)

Adamic-Adar index of u and :None:None:`v` is defined as

$$\sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{1}{\log |\Gamma(w)|}$$

where $\Gamma(u)$ denotes the set of neighbors of $u$. This index leads to zero-division for nodes only connected via self-loops. It is intended to be used when no self-loops are present.

Parameters

G : graph

NetworkX undirected graph.

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

Adamic-Adar index 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 non-existent edges in the graph will be used. Default value: None.

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 Adamic-Adar index.

Compute the Adamic-Adar index of all node pairs in ebunch.

Examples

>>> G = nx.complete_graph(5)
... preds = nx.adamic_adar_index(G, [(0, 1), (2, 3)])
... for u, v, p in preds:
...  print(f"({u}, {v}) -> {p:.8f}") (0, 1) -> 2.16404256 (2, 3) -> 2.16404256
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.link_prediction.adamic_adar_index

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /networkx/algorithms/link_prediction.py#153
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