The graph isomorphism problem deals with the question of whether there exists a bijective mapping between any two graphs that preserves the adjacency of their vertices. This is one of the rare known problems for which the question of their classification into the complexity classes P or NP-complete is still open.
A heuristic algorithm nauty is presented, which transforms the problem into a search for the canonical form. Through a process of gradually coloring nodes, the algorithm refines the distinction between them, thereby constructing a tree of candidates for the canonical form. Similar ideas are also employed by other practical algorithms. Although they lack a guarantee of a fast performance for all graphs, it turns out that this is the case in most instances.
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