square_clustering#

square_clustering(G, nodes=None)[source]#

计算节点的平方聚类系数。

对于每个节点，返回存在的平方数与可能的平方数的比例 [1]

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

其中 \(q_v(u,w)\) 是 \(u\) 和 \(w\) 除了 \(v\) 之外的共同邻居数（即平方数），而 \(a_v(u,w) = (k_u - (1+q_v(u,w)+\theta_{uv})) + (k_w - (1+q_v(u,w)+\theta_{uw}))\) ，其中 \(\theta_{uw} = 1\) 如果 \(u\) 和 \(w\) 相连，否则为 0。 [2]

Parameters:

G图
nodes节点容器，可选（默认=G中的所有节点）: 计算容器中节点的聚类系数。

Returns:

c4字典: 一个以节点为键，平方聚类系数值为值的字典。

Notes

虽然 \(C_3(v)\) （三角形聚类）给出了节点 v 的两个邻居相互连接的概率，但 \(C_4(v)\) 是节点 v 的两个邻居共享一个不同于 v 的共同邻居的概率。此算法可应用于二分图和单分图网络。

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”

parallelParallel backend for NetworkX algorithms

The nodes are chunked into node_chunks and then the square clustering coefficient for all node_chunks are computed in parallel over all available 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 chunks, where n is the number of CPU cores.

[Source]