  This paper develops two heuristic algorithms to solve graph isomorphism,
using free energy encoding. The first algorithm uses four types of encoding
refinement techniques such that every graph can be distinguished by a canonical
number computed by the algorithm. The second algorithm injects energy into the
graph to conduct individualization such that the correspondence relation
between a pair of isomorphic graphs can be found. The core principle behind the
two algorithms is encoding discrete structures as real numbers. A large set of
experiments demonstrated the effectiveness of our algorithms.
