We introduce the definition of Social Leader that gives a local centrality measure for each node in a graph. A node a is a Social Leader if the number of cycles of length 3 passing through u is greater than the corresponding number for its neighbors. This concept is used to visualize large graphs, identify influent agents in social networks (word of mouth effect) and find communities.
Blondel, V., de Kerchove D’Exaerde, C., Huens, E., & Van Dooren, P. (2006). Social leaders in graphs. Lecture Notes in Control and Information Sciences, 341, 231-237. https://doi.org/10.1007/3-540-34774-7_30 (Original work published 2006)