Consequences of Connection Failure - Centrality and the Importance for Cohesion

This paper suggests a new approach for centrality measures for general (weighted) networks taking into account the importance for cohesion and relative power of connections. While existing literature either ignores the importance for cohesion or measures it by analyzing consequences arising from the failure of whole nodes, this approach analyzes consequences of tie failures. Using cooperative game theory, we assign weights to every tie of the network where the cooperative game accounts for the cohesion of the network. These weights are combined with the weights of the original network where emphasis for the latter and for cohesion can be regulated individually. Then, the degree measure and Eigenvector measure are applied. This provides the first centrality approach accounting for cohesion and relative importance/power of connections. We provide axiomatic characterizations for the degreebased measures in the case of binary networks and discuss computational complexity. Furthermore, we give examples discussing the drawbacks of existing measures in contrast to our suggested one and as a political application, we show how our Approach can be used to forcast government formation by the case of the state parliament election in Hamburg, Germany.