Multi-scale Community Detection In Complex Networks

Network science is an emerging science.The network abstracts all aspects of the real world into elements and links between elements.The abstract results are often intricate and cannot be summarized by simple mathematical rules.They have this topology,that is,complex networks.Community property is an important feature of complex networks after small-world and scale-free properties.Therefore,community detection is of theoretical and practical significance.Community is not only a single scale,often a large community contains more small communities,in other words,the structure of the community is multi-level.In order to explore the multi-scale characteristics of the network,the research of this paper is carried out.The work of this paper is mainly divided into two aspects:(1)Multi-scale community detection based on node similarity.By selecting three node similarity indexes,the multi-scale characteristics of the network are studied based on the node similarity community detection algorithm used in this paper.In this paper,it is pointed out that the community hierarchy is related to the range of similarity threshold.By adjusting the range,the community structure at different scales can be obtained.Through empirical analysis on real network data and artificial network data.By analyzing the specific community detection characteristics of different indicators,it is found that the results obtained by each indicator are different.Through in-depth analysis of the advantages and disadvantages of each similarity indicator in multi-scale community identification.(2)The Louvain algorithm with modularity function F2 constraint is used to detect communities.Both some multi-scale community detection methods and community detection algorithms based on Newman modularity function Q cannot avoid the resolution limit problem of community detection.In order to overcome the resolution limit problem,a new modularity function F2 is proposed.It is theoretically proved that the proposed modularity function F2 can detect community structure better than other objective functions Q,D,F and M.Through empirical analysis on network data sets and other objective functions,the results show that the algorithm is feasible.Finally,by comparing the results of community detection with and without modularity function F2 constraints,it is found that the Louvain algorithm with modularity function constraints has better performance.