Symmetry Measures on Complex Networks

Abstract

As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we take network structures, its symmetry means invariance of adjacency of nodes under the permutations on node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure, if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs.