Analysis About Modularity Of Complex Networks

Complex network is the abstract of complex system.The nodes are the individualities and edge are relationships between nodes according to some natural or artificial rules. Complex network is different from the regular networks and random networks, with small world, scale-free, and community structure.Detecting communities in the network has important practical applications,in recent years,a great progress has been made in the community detection algorithm. In order to measure the quality of the community, Newman and Grivan proposed the concept of modularity. This standard can be used in many algorithms. But the study found that the standard has limitations and can not find small communities, even though these communities are strongly connected. Besides, Random network has a large modularity. Therefore, a new standard is needed.This article describes the modularity of different networks, find the limitations of modularity, and give the measures. In practice, when find the community structure, we can adjust the Hamiltonian parameters to get a reasonable segmentation.Also, modularity density can overcome the limitations, but it's a new limit, the network can not be broken down into two communities. Weakest community is produced based on on weak and strong communities communitiy.At last analysis of the relationship between the three kinds of community structures.