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 $a_{v} (u, w) = (k_{u} - (1 + q_{v} (u, w) + θ_{u v})) + (k_{w} - (1 + q_{v} (u, w) + θ_{u w}))$ , where $θ_{u w} = 1$ if $u$ and $w$ are connected and 0 otherwise. [2]

Parameters:

Ggraph
nodescontainer of nodes, optional (default=all nodes in G): Compute clustering for nodes in this container.

Returns:

c4dictionary: A dictionary keyed by node with the square clustering coefficient value.

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.

[2]

Zhang, Peng et al. Clustering Coefficient and Community Structure of Bipartite Networks. Physica A: Statistical Mechanics and its Applications 387.27 (2008): 6869–6875. https://arxiv.org/abs/0710.0117v1

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}
----

Additional backends implement this function

graphblasOpenMP-enabled sparse linear algebra backend.

Additional parameters:

chunksizeint or str, optional: Split the computation into chunks; may specify size as string or number of rows. Default “256 MiB”

parallelA networkx backend that uses joblib to run graph algorithms in parallel. Find the nx-parallel’s configuration guide here

The nodes are chunked into node_chunks and then the square clustering coefficient for all node_chunks are computed in parallel over n_jobs number of CPU cores.

Additional parameters:

get_chunksstr, function (default = “chunks”): A function that takes in a list of all the nodes (or nbunch) as input and returns an iterable node_chunks. The default chunking is done by slicing the nodes into n_jobs number of chunks.

[Source]