Replicator equations, maximal cliques, and graph isomorphism

Wie present a new energy-minimization framework for the graph isomorphism problem which is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus ill the mid-1990s, and recently expanded ill various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. To solve the program we use "replicator'' equations, a class of simple continuous- and discrete-time dynamical systems developed ill various branches of theoretical biology. We show how, despite their inability to escape from local solutions, they nevertheless provide experimental results which are competitive with those obtained using more elaborate mean-field annealing heuristics.