A Survey on Optimization Studies of Group Centrality Metrics
Mustafa Can Camur, Chrysafis Vogiatzis
TL;DR
This paper surveys the evolution of group centrality metrics from an optimization and operations research perspective, tracing foundational ideas to recent probabilistic and stochastic approaches. It catalogues node-group centrality definitions for group degree, group betweenness, and group closeness, and it classifies structures (clique, star, representative set, walk) that shape how centrality is computed and optimized. The authors map the landscape of solution techniques, highlighting MILP formulations, combinatorial branch-and-bound, and decomposition methods, and they identify gaps where probabilistic models and stochastic optimization are underexplored. The work provides a structured roadmap for applying group centrality in real-world networks and points to fertile directions for future OR research, including uncertainty-aware methods and broader motif definitions.
Abstract
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.