The connections of connections : new results on the centrality and communicability of networks

Abstract

In network science, the centrality, or importance, of a node in a network is of crucial importance, for instance to rank webpages or to measure the rate of the spread of news on a social network. Also of importance is measuring the communicability between two nodes in a network, which assesses how well the nodes can communicate between them. Two methods of calculating the centrality and communicability of nodes in a network, arising from the subgraph centrality approach utilizing walk of graphs are surveyed, with a focus on the more recently introduced of these two methods. A connection between the centrality and communicability scores produced by this scheme is presented. The question of how the centrality and communicability of nodes vary by the introduction of new links in the network is put forward. To answer this question, formulae that derive these centrality and communicability differences in terms of existing centralities of nodes within the network are presented.