A Concentration of Measure Approach to Correlated Graph Matching

The graph matching problem emerges naturally in various applications such as Web privacy, image processing and computational biology. In this article, is considered under a stochastic model, where pair of randomly generated graphs with pairwise correlated edges are to be matched that given the labeling vertices first graph, labels second recovered by leveraging correlation among their edges. settings models. step, Correlated Erdos-Renyi (CER) model studied, all edge pairs whose have similar based on identical distributions independently other A scheme called typicality introduced. operates investigating joint adjacency matrices two graphs. New results permutations sequences lead necessary sufficient conditions for successful parameters CER model. next extended community structure Stochastic Block Model (SBM). SBM generalization each vertex associated label, which affects its statistics. further ensembles more than Lastly, seeded investigated subset known prior matching. scenario, addition obtaining matching, polynomial time algorithm proposed.