Graph Isomorphism

In this article we review some of the most relevant properties related to graph isomorphism and graph components. We start by introducing some concepts related to graph traversal (walks, paths, cycles, circuits), then we introduce two natural concepts related to connectivity: connected and strongly connected components. We consider then the definition of graph isomorphism and clique, and problems related to subgraph isomorphism and motif detection, like maximal clique, maximum clique and clique relaxations. We review two approaches that have widely applied to study graphs: network topology measures (average path length, diameter, cluster coefficient, degree distribution), centralization measures (degree centrality, closeness centrality, betweenness centrality, eigenvector centrality).