A novel subgraph $$K^{+}$$-isomorphism method in social network based on graph similarity detection

In this paper, we propose a novel \(K^{+}\)-isomorphism method to achieve K-anonymization state among subgraphs or detected communities in a given social network. Our proposed \(K^{+}\)-isomorphism method firstly partitions the subgraphs we have detected into some similar-subgraph clusters followed by graph modification conducted in every cluster. In this way, it is feasible to publish preserved structures of communities or subgraphs and every preserved structure actually represents a cluster of at least K subgraphs or communities which are isomorphic to each other. The contributions of this paper are listed as follows: On the one hand, we improve a maximum common subgraph detection algorithm, MPD\(_{-}\)V, which is a core technique for graph similarity detection involved in partition phase of our proposed \(K^{+}\)-isomorphism method; on the other hand, with minor adjustment, we utilize some current techniques as an innovative combination to finish the partition and modification of similar-community cluster in \(K^{+}\)-isomorphism method. The experiments have shown that the improved MPD\(_{-}\)V method has much better efficiency to search larger common subgraphs with acceptable performance compared with its prototype and other techniques. Moreover, our proposed \(K^{+}\)-isomorphism method can achieve the K-isomorphism state with less modification of original network structure, or lower anonymization cost compared to the current K-isomorphism method.