Significance of Side Information in the Graph Matching Problem

TL;DR

This paper explores how different types of side information, like community labels and imperfect matchings, can enhance graph matching algorithms, especially under attack scenarios and with limited seed data.

Contribution

It introduces new algorithms leveraging community labels and imperfect matchings, and analyzes their effectiveness in graph matching with side information.

Findings

Communities significantly improve matching accuracy with few seeds.

Proposed algorithms outperform baseline methods in experiments.

Community information is especially valuable in weakly correlated networks.

Abstract

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.