A Survey on Optimization Studies of Group Centrality Metrics

Centrality metrics have become a popular concept in network science andoptimization. Over the years, centrality has been used to assign importance andidentify influential elements in various settings, including transportation,infrastructure, biological, and social networks, among others. That said, mostof the literature has focused on nodal versions of centrality. Recently, groupcounterparts of centrality have started attracting scientific and practitionerinterest. The identification of sets of nodes that are influential within anetwork is becoming increasingly more important. This is even more pronouncedwhen these sets of nodes are required to induce a certain motif or structure.In this study, we review group centrality metrics from an operations researchand optimization perspective for the first time. This is particularlyinteresting due to the rapid evolution and development of this area in theoperations research community over the last decade. We first present ahistorical overview of how we have reached this point in the study of groupcentrality. We then discuss the different structures and motifs that appearprominently in the literature, alongside the techniques and methodologies thatare popular. We finally present possible avenues and directions for futurework, mainly in three areas: (i) probabilistic metrics to account forrandomness along with stochastic optimization techniques; (ii) structures andrelaxations that have not been yet studied; and (iii) new emerging applicationsthat can take advantage of group centrality. Our survey offers a concise reviewof group centrality and its intersection with network analysis andoptimization.