Regular Equivalence for Social Networks

Networks and graphs are highly relevant in modeling real-life communities and their interactions. In order to gain insight in their structure, different roles are attributed to vertices, effectively clustering them in equivalence classes. A new formal definition of regular equivalence is presented in this paper, and the relation with other equivalence types is investigated and mathematically proven. An efficient algorithm is designed, able to detect all regularly equivalent roles in large-scale complex networks. We apply it to both Barabasi-Albert random networks, as well as real-life social networks, which leads to interesting insights.