Compute the clustering coefficient for nodes.
For unweighted graphs the clustering of each node u is the fraction of possible triangles that exist, For each node find the fraction of possible triangles that exist,
c_u = \frac{2 T(u)}{deg(u)(deg(u)-1)},
where T(u) is the number of triangles through node u and deg(u) is the degree of u.
For weighted graphs the clustering is defined as the geometric average of the subgraph edge weights [R158],
c_u = \frac{1}{deg(u)(deg(u)-1))} \sum_{uv} (\hat{w}_{uv} \hat{w}_{uw} \hat{w}_{vw})^{1/3}.
The edge weights \hat{w}_{uv} are normalized by the maximum weight in the network \hat{w}_{uv} = w_{uv}/\max(w).
The value of c_u is assigned to 0 if deg(u) < 2.
Parameters : | G : graph nodes : container of nodes, optional (default=all nodes in G)
weight : string or None, optional (default=None)
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Returns : | out : float, or dictionary
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Notes
Self loops are ignored.
References
[R158] | (1, 2) Generalizations of the clustering coefficient to weighted complex networks by J. Saramäki, M. Kivelä, J.-P. Onnela, K. Kaski, and J. Kertész, Physical Review E, 75 027105 (2007). http://jponnela.com/web_documents/a9.pdf |
Examples
>>> G=nx.complete_graph(5)
>>> print(nx.clustering(G,0))
1.0
>>> print(nx.clustering(G))
{0: 1.0, 1: 1.0, 2: 1.0, 3: 1.0, 4: 1.0}