CREST, JST, Kawaguchi Center Building, 4-1-8, Honcho, Kawaguchi-shi, Saitama, 332-0012, Japan.
Department of Engineering Mathematics, Merchant Venturers Building, University of Bristol, Woodland Road, Clifton, Bristol, BS8 1UB, United Kingdom.
Sci Rep. 2018 May 9;8(1):7351. doi: 10.1038/s41598-018-25560-z.
Many empirical networks have community structure, in which nodes are densely interconnected within each community (i.e., a group of nodes) and sparsely across different communities. Like other local and meso-scale structure of networks, communities are generally heterogeneous in various aspects such as the size, density of edges, connectivity to other communities and significance. In the present study, we propose a method to statistically test the significance of individual communities in a given network. Compared to the previous methods, the present algorithm is unique in that it accepts different community-detection algorithms and the corresponding quality function for single communities. The present method requires that a quality of each community can be quantified and that community detection is performed as optimisation of such a quality function summed over the communities. Various community detection algorithms including modularity maximisation and graph partitioning meet this criterion. Our method estimates a distribution of the quality function for randomised networks to calculate a likelihood of each community in the given network. We illustrate our algorithm by synthetic and empirical networks.
许多实证网络具有社区结构，其中节点在每个社区（即一组节点）内密集地相互连接，而在不同社区之间稀疏连接。与网络的其他局部和中等尺度结构一样，社区在大小、边密度、与其他社区的连接性和重要性等方面通常是异构的。在本研究中，我们提出了一种方法来统计检验给定网络中单个社区的显著性。与以前的方法相比，本算法的独特之处在于它接受不同的社区检测算法和单个社区的相应质量函数。本方法要求可以量化每个社区的质量，并且社区检测是作为对社区之间的此类质量函数的优化来执行的。各种社区检测算法，包括模块化最大化和图划分，都满足这个标准。我们的方法通过随机网络来估计质量函数的分布，以计算给定网络中每个社区的可能性。我们通过合成和经验网络来说明我们的算法。
