Since the beginning of the research on the dynamics of complex networks, the deep relationship between topology and dynamics has been thoroughly explored with regard the synchronization between the nodes’ dynamics, and the knowledge gathered so far has driven the advance in crucial applications.
Most literature on measuring the symmetry of networks uses graph automorphism algorithms to find the automorphism group, and defines either the number of elements in the automorphism group or the number of nodes involved in the automorphism group as a measure of the level of symmetry of networks.
Percolation is an emblematic model used to understand the robustness of interconnected systems, in which the nodes of a network are removed and different topological properties of the resulting topological structure are analyzed.