Network community detection using modified modularity criterion

Abstract

The aim of the research. The object of this study is complex networks whose model is undirected weighted ordinary (without loops and multiple edges) graphs. The task to detect communities, that is, par¬tition the set of network nodes into communities, has been considered. It is assumed that such communities should be non-overlapped. At present, there are many approaches to solving this task and, accordingly, many methods that imple¬ment it. Methods based on the maximization of the network modularity function have been considered. A modified modu¬larity criterion (function) has been proposed. The value of this criterion explicitly depends on the number of nodes in the com¬munities. The partition of network nodes into communities with maximization by such a criterion is significantly more prone to the detection of small communities, or even singleton-node communities. This property is a key characteristic of the pro¬posed method and is useful if the network being analyzed really has small communities. In addition, the proposed modularity cri¬terion is normalized with respect to the current number of com¬munities. This makes it possible to compare the modularity of network partitions into different numbers of communities. This, in turn, makes it possible to estimate the number of communi¬ties that are formed, in cases when this number is not known a priori. A method for partitioning network nodes into commu¬nities based on the criterion of maximum modularity has been devised. The corresponding algorithm is suboptimal, belongs to the class of greedy algorithms, and has a low computational complexity – linear with respect to the number of network nodes. As a result, it is fast, so it can be used for network parti¬tioning. Conclusion. The method devised for detecting network communities was tested on classic datasets, which confirmed the effective¬ness of the proposed approach