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average_clustering

clustering

clustering(G, nodes=None, weight=None)[source]

Compute the clustering coefficient for nodes.

For unweighted graphs the clustering of each node

System Message: WARNING/2 (u)

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is the fraction of possible triangles that exist, For each node find the fraction of possible triangles that exist,

System Message: WARNING/2 (c_u = \frac{2 T(u)}{deg(u)(deg(u)-1)},)

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where

System Message: WARNING/2 (T(u))

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is the number of triangles through node

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and

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is the degree of

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.

For weighted graphs the clustering is defined as the geometric average of the subgraph edge weights [R158],

System Message: WARNING/2 (c_u = \frac{1}{deg(u)(deg(u)-1))} \sum_{uv} (\hat{w}_{uv} \hat{w}_{uw} \hat{w}_{vw})^{1/3}.)

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The edge weights

System Message: WARNING/2 (\hat{w}_{uv})

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are normalized by the maximum weight in the network

System Message: WARNING/2 (\hat{w}_{uv} = w_{uv}/\max(w))

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.

The value of

System Message: WARNING/2 (c_u)

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is assigned to 0 if

System Message: WARNING/2 (deg(u) < 2)

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.

Parameters :

G : graph

nodes : container of nodes, optional (default=all nodes in G)

Compute clustering for nodes in this container.

weight : string or None, optional (default=None)

The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1.

Returns :

out : float, or dictionary

Clustering coefficient at specified nodes

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}