Vulnerability and power on networks

Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of networks. We establish an unexpected connection between network vulnerability and graph regularizability. We use the Shapley value of coalition games to introduce fresh notions of vulnerability and power at node level defined in terms of the corresponding measures at group level. We investigate the computational complexity of computing the defined measures, both at group and node levels, and provide effective methods to quantify them. Finally we test vulnerability and power on both artificial and real network

Distances and Domination in Graphs

This book presents a compendium of the 10 articles published in the recent Special Issue “Distance and Domination in Graphs”. The works appearing herein deal with several topics on graph theory that relate to the metric and dominating properties of graphs. The topics of the gathered publications deal with some new open lines of investigations that cover not only graphs, but also digraphs. Different variations in dominating sets or resolving sets are appearing, and a review on some networks’ curvatures is also present