Attachment Centrality: An Axiomatic Approach to Connectivity in Networks

Centrality indices aim to quantify the importance of nodes or edges in a network. A number of new centrality indices have recently been proposed to try and capture the role of nodes in connecting the network. While these indices seem to deliver new insights, to date not enough is known about their theoretical properties. To address this issue, we propose an axiomatic approach. Specifically, we prove that there exists a unique centrality index satisfying some intuitive properties related to network connectivity. This new index, which we call Attachment Centrality, is equivalent to the Myerson value of a particular graph-restricted coalitional game. Building upon our theoretical analysis, we show that our Attachment Centrality has certain computational properties that are more attractive than the Myerson value for an arbitrary game.