networkx.algorithms.cluster.square_clustering

square_clustering(G, nodes=None)

Compute the squares clustering coefficient for nodes.

For each node return the fraction of possible squares that exist at the node 1

$$C_4(v) = \frac{ \sum_{u=1}^{k_v} \sum_{w=u+1}^{k_v} q_v(u,w) }{ \sum_{u=1}^{k_v} \sum_{w=u+1}^{k_v} [a_v(u,w) + q_v(u,w)]},$$

where $q_v(u,w)$ are the number of common neighbors of $u$ and $w$ other than $v$ (ie squares), and $a_v(u,w) = (k_u - (1+q_v(u,w)+\theta_{uv}))(k_w - (1+q_v(u,w)+\theta_{uw}))$, where $\theta_{uw} = 1$ if $u$ and $w$ are connected and 0 otherwise.

Parameters

• G (graph)

• nodes (container of nodes, optional (default=all nodes in G)) – Compute clustering for nodes in this container.

Returns

c4 – A dictionary keyed by node with the square clustering coefficient value.

Return type

dictionary

Examples

>>>

>>> G = nx.complete_graph(5)
>>> print(nx.square_clustering(G, 0))
1.0
>>> print(nx.square_clustering(G))
{0: 1.0, 1: 1.0, 2: 1.0, 3: 1.0, 4: 1.0}

Notes

While $C_3(v)$ (triangle clustering) gives the probability that two neighbors of node v are connected with each other, $C_4(v)$ is the probability that two neighbors of node v share a common neighbor different from v. This algorithm can be applied to both bipartite and unipartite networks.

References

1

Pedro G. Lind, Marta C. González, and Hans J. Herrmann. 2005 Cycles and clustering in bipartite networks. Physical Review E (72) 056127.