On reliability indices of communication networks

The aim of this paper is to study the global reliability of communication networks. We assume that, in a communication network, the weights of the edges quantify the volume or the quality of the information transmitted by the nodes. In such a case, the strength of a path (resp. walk), called the reliability of the path (resp. walk) can be calculated as the product of the weights of the edges belonging to the paths (resp. walks). We introduce three indices to compute the reliability of a digraph (resp. graph). The first one is a version of Wiener index where we consider only the most reliable path between each pair of nodes. The second notion of reliability index considers reliability of all walks between each pair of nodes instead of taking into account only the most reliable path. The last one is a generalization of the functional centralization to the case of weighted networks. In this case, the notion of reliability index considers, for each node, the reliability of all closed walks starting and ending in the node. In addition, we propose a method for computing the introduced indices. Application of some of the proposed indices to trust-weighted social networks is also discussed.