A Centrality Measure for Networks With Community Structure Based on a Generalization of the Owen Value

There is currently much interest in the problem of measuring the centrality of nodes in networks/graphs; such measures have a range of applications, from social network analysis, to chemistry and biology. In this paper we propose the first measure of node centrality that takes into account the community structure of the underlying network. Our measure builds upon the recent literature on game-theoretic centralities, where solution concepts from cooperative game theory are used to reason about importance of nodes in the network. To allow for flexible modelling of community structures, we propose a generalization of the Owen value—a well-known solution concept from cooperative game theory to study games with a priori-given unions of players. As a result we obtain the first measure of centrality that accounts for both the value of an individual node’s relationships within the network and the quality of the community this node belongs to.