  Centrality metrics have become a popular concept in network science and
optimization. Over the years, centrality has been used to assign importance and
identify influential elements in various settings, including transportation,
infrastructure, biological, and social networks, among others. That said, most
of the literature has focused on nodal versions of centrality. Recently, group
counterparts of centrality have started attracting scientific and practitioner
interest. The identification of sets of nodes that are influential within a
network is becoming increasingly more important. This is even more pronounced
when these sets of nodes are required to induce a certain motif or structure.
In this study, we review group centrality metrics from an operations research
and optimization perspective for the first time. This is particularly
interesting due to the rapid evolution and development of this area in the
operations research community over the last decade. We first present a
historical overview of how we have reached this point in the study of group
centrality. We then discuss the different structures and motifs that appear
prominently in the literature, alongside the techniques and methodologies that
are popular. We finally present possible avenues and directions for future
work, mainly in three areas: (i) probabilistic metrics to account for
randomness along with stochastic optimization techniques; (ii) structures and
relaxations that have not been yet studied; and (iii) new emerging applications
that can take advantage of group centrality. Our survey offers a concise review
of group centrality and its intersection with network analysis and
optimization.
