Measuring the significance of community structure in complex networks

Abstract

Many complex systems can be represented as networks and separating a network into communities could simplify the functional analysis considerably. Recently, many approaches have been proposed for finding communities, but none of them can evaluate the communities found are significant or trivial definitely. In this paper, we propose an index to evaluate the significance of communities in networks. The index is based on comparing the similarity between the original community structure in network and the community structure of the network after perturbed, and is defined by integrating all the similarities. Many artificial networks and real-world networks are tested. The results show that the index is independent from the size of network and the number of communities. Moreover, we find the clear communities always exist in social networks, but don't find significative communities in proteins interaction networks and metabolic networks. The study of the community structure of networks has become a very important part of researches of complex networks. Nodes belonging to a tight-knit community are more likely to have particular properties in common. In social relationship network, communities usually represent different friend subgroups. In the world wide web, community analysis has uncovered thematic clusters. In biochemical or neural networks, different communities may represent different functional groups, and separating the network into such groups could simplify the functional analysis considerably. As a result, the problem of identification of communities has been the focus of many recent efforts. So two questions are proposed, the first is, how to detected communities in the networks? In recent studies, plenty of algorithms are proposed [1,2,3,4, 5,6,7,8,9,10,11,12,13,14,15] (see [5] as a review). The second question is coming hand in hand with the first question: how to evaluate the communities detected? We believe that there exist clear communities in some networks while no clear communities in the other networks. But almost all algorithms could find the "community structure" in networks in their ways, without thinking about whether the community structure actually exists or not. Even many algorithms can also find the community in random networks, in which are considered having no community. For the existence of such a situation, the discussion on the "significative communities" is needed. As a network is given, it is meaningless to detect the community when the community structure is not significative at all.Scientists try to propose a universal index to evaluate the partitions. And the modularity Q [16] was presented as an index of community structure and by now it has been widely accepted [5,10,11,14] as a measure for the community structure. Modularity Q was presented as * yanqing.hu.sc@gmail.com † zdi@bnu.edu.com a index of community structure by Newman and Grive, which was introduced as Q = r (e rr − a 2 r ), where e rr are the fraction of links that connect two nodes inside the community r, a r the f...

Detecting the optimal number of communities in complex networks

“…3.6 Measuring the significance of community structures Many efficient methods have been proposed for finding communities, but few of them can evaluate the communities found are significant or trivial definitely [16]. In some works the concept of significance has been related to that of robustness or stability of a partition against random perturbations of the graph structure.…”

“…A number of indexes for measuring similarities or differences between partitions of a network have been proposed in the past [13,15,16,17,18,19,20,21]. Our method here follows the information theoretic methods.…”

“…In this paper, we propose a suitable method for evaluating the optimal number of the communities based on measuring the precision of algorithms and closely relating to the accuracy of algorithms. We first use the algorithm based on mixture model,which proposed by Newman and Leicht [14], to induce a sequence P(k)(1 ≤ k ≤ n) of divisions into communities; Second, we measure the precision of the algorithm based on "information entropy", which has been used to evaluate the similarity of communities [15,16,17,18]; At last, we use our proposed index Ω(c) to find the optimal number of the communities. Our statistic is an auxiliary method which can be applied to almost all the algorithms with random characteristics to help them find the optimal community number.…”

Exploring community structure of software Call Graph and its applications in class cohesion measurement

“…A group of approaches have been proposed with the basic understanding that the significance of community can be quantified by the robustness or stability of community structure against random perturbations (Karrer et al, 2008;Hu et al, 2010;Lancichinetti et al, 2010). Intuitively, if a network has significant community structure, such structure should be robust to perturbation.…”

The comparison of significance of fuzzy community partition across optimization methods

“…It is essential to establish a detail framework analyzing the significance of community structure, since real networks own specific characteristics [5,10,29]. In this section, we discuss these important characteristics and give a detailed introduction of the framework.…”