Anti-modularity and anti-community detecting in complex networks

•We present the anti-modularity as a quality measure of the anti-community detecting.•A label propagation algorithm LPAD for anti-community detection is proposed.•The proposed algorithm LPAD does not require the predefined number of anti-communities.•The proposed algorithm LPAD has low time complexity of O(n2).•LPAD can maximize the number of edges between clusters and minimize the number of clusters.

Many networks of interest in sciences and social research can be divided naturally into anti-communities. The problem of detecting and characterizing such anti-community structure has attracted recent attention. In this paper, we first define the anti-modularity as a quantitative measure of anti-community partitioning on a network. We also theoretically and empirically show the reliability of anti-modularity as a measurement of the quality of an anti-community partitioning. A label propagation algorithm LPAD for anti-community detection is proposed. Experimental results on synthetic and real world networks show that our algorithm LPAD can obtain higher quality anti-community partitioning than other methods.