A description algorithm for community structure

In the last decade, a large number of graph mining algorithms have been proposed. But there are only a few descriptions about community structure. The communities in different network have different structure, and even in the same network the communities may have different community structure. If we can't describe the community structure reasonably, it is difficult to use the communities which are gotten from the community detection algorithms. Many community detection algorithms may have no meaning. In this paper, the community structure would be described from four different aspects. They are inside properties which describe the community in terms of the community itself, outside properties which describe the community in terms of relationship between communities, level properties which describe community in terms of relationship between the large community and the small communities which compose to the large community at different level, and dynamic properties which describe the evolution information of the communities in different time. Futher, a description algorithm based on the statistic is proposed. In this description algorithm, the community structure information can be descriped in detail and can be used for futher analysis. Also, the community structure can be described in different levels by choosing different statistic rules. A data structure is also proposed to save the community structure information for the purpose of searching it quickly.