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...
