Novel centrality metrics for studying essentiality in protein-protein interaction networks based on group structures

In this work, we introduce centrality metrics based on group structures, and we show their performance in estimating importance in protein-protein interaction networks (PPINs). The centrality metrics introduced are extensions of well-known nodal metrics. However, instead of focusing on a single node, we focus on that node and the set of nodes around it. Furthermore, we require the set of nodes to induce a specific pattern or structure. The structures investigated range from the “stricter“ induced stars and cliques, to a “looser” definition of a representative structure. We derive the computational complexity of all metrics and provide mixed integer programming formulations; due to the problem complexity and the size of PPINs, using commercial solvers is not always viable. Hence, we propose a combinatorial branch-and-bound solution approach. We conclude by showing the effectiveness of the proposed metrics in identifying essential proteins in Helicobacter pylori and comparing them to nodal metrics.