clustering

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

Compute the clustering coefficient for nodes.

For unweighted graphs, the clustering of a node u is the fraction of possible triangles through that node 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 [1],

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)) – 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 – Clustering coefficient at specified nodes

Return type:

float, or dictionary

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}

Notes

Self loops are ignored.

References

[1]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