networkx.algorithms.cluster.square_clustering¶
-
square_clustering(G, nodes=None)[source]¶ 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.