Graph matching is a generalization of the classic graph isomorphism problem. By using only their structures a graph-matching algorithm finds a map between the vertex sets of two similar graphs. This has applications in the deanonymization of social and information networks and, more generally, in the merging of structural data from different domains. One class of graph-matching algorithms starts with a known seed set of matched node pairs. Despite the success of these algorithms in practical applications, their performance has been observed to be very sensitive to the size of the seed set. The lack of a rigorous understanding of parameters and performance makes it difficult to design systems and predict their behavior. In this paper, we propose and analyze a very simple percolation -based graph matching algorithm that incrementally maps every pair of nodes (i, j) with at least r neighboring mapped pairs. The simplicity of this algorithm makes possible a rigorous analysis that relies on recent advances in bootstrap percolation theory for the G(n, p) random graph. We prove conditions on the model parameters in which percolation graph matching succeeds, and we establish a phase transition in the size of the seed set. We also confirm through experiments that the performance of percolation graph matching is surprisingly good, both for synthetic graphs and real social-network data.
Recent work also sheds light on the performance of this approach, and establishes a sharp phase transition in the size of the seed set between a regime where the algorithm almost certainly fails, and a regime when it succeeds in matching almost everything REF .
On the performance of percolation graph matching
COSN '13
Computer Science