Community structure testing by counting frequent common neighbor sets

The detection of communities from a graph is a key issue in network science and graph data mining. However, existing community detection algorithms can always partition a given network/graph into different communities/subgraphs, even when no community structure exists. Obviously, it will lead to fruitless efforts and erroneous conclusions if we conduct the community detection procedure on a network without a community structure. Hence, prior to community detection, it is a must to test whether the community structure is present in the target network. Unfortunately, the community structure testing issue is still not revolved and existing solutions have some limitations. Therefore, we present a new test, which is called FCN (Frequent Common Neighbor) test to tackle the community structure testing problem. In FCN test, the number of FCN sets is employed as the test statistic, which will approximately follows a Poisson distribution when the support threshold is sufficiently large under the null hypothesis that the graph is generated according to the Erdős-Rényi model. We compare the proposed FCN test with existing community structure testing methods on both real networks and simulated networks. The experimental results demonstrate the effectiveness and advantage of our method.