Significance of Side Information in the Graph Matching Problem

Percolation based graph matching algorithms rely on the availability of seed vertex pairs as side information to efficiently match users across networks. Although such algorithms work well in practice, there are other types of side information available which are potentially useful to an attacker. In this paper, we consider the problem of matching two correlated graphs when an attacker has access to side information, either in the form of community labels or an imperfect initial matching. In the former case, we propose a naive graph matching algorithm by introducing the community degree vectors which harness the information from community labels in an efficient manner. Furthermore, we analyze a variant of the basic percolation algorithm proposed in literature for graphs with community structure. In the latter case, we propose a novel percolation algorithm with two thresholds which uses an imperfect matching as input to match correlated graphs. We evaluate the proposed algorithms on synthetic as well as real world datasets using various experiments. The experimental results demonstrate the importance of communities as side information especially when the number of seeds is small and the networks are weakly correlated.