A Subgraph Isomorphism-based Attack Towards Social Networks

Abstract

It has been widely recognized that social network analysis of group relationships and behaviors come to thrive, so publicity social networks have gained growing attention from third-party individuals for academic researchers and advertisers. Anonymous versions are generally obtained from the naive anonymization mechanism through identity transformation to fend off attacks on socially sensitive information. The adversaries intend to implement person re-identification in anonymous data, and they generally possess a subset of social interaction information of the target user. In this way, a privacy breach could be achieved by exploiting the neighbourhood of the object's known structural information. Say, if one node's information is breached, other nodes’ private information will be compromised according to the detected structural information. Therefore, all the mentioned above are equivalent to the subgraph isomorphism problem to identify who is who in the social networks. Existing enumeration and indexing-related subgraph isomorphism methods cannot process matching problems with both large target and query graphs. Therefore, subgraph querying is a knotty problem pressing for a solution. In this work, we elaborate on the subgraph of structural attack. Our subgraph isomorphism-based method adopts a 3-stage framework for learning and refining structural correspondences over a large graph. First, we generate a set of candidate matches and compare the query graph with these candidate graphs over the corresponding number of vertex and edge, which can noticeably reduce the number of candidate graphs. Secondly, we employ the permutation theorem to evaluate the row sum of vertex and edge adjacency matrix of query graph and candidate graph. Lastly, our proposed scheme deploys the well-found equinumerosity theorem to verify if the query graph and candidate graph satisfy the isomorphic relationship. Solid evaluation criteria on time complexity verify the proposed attack strategy.