Network reliability analysis with link and nodal weights and auxiliary nodes

Networks are omnipresent, with examples in many different fields, from biological networks (such as the nervous and cardiovascular system) to physical networks (such as roadways, railways, and electrical power and water supply systems) to technological networks (such as the World Wide Web) and social network (such as the community network among people or animals). This paper proposes a novel probabilistic methodology to quantify the network reliability based on existing (diameter and efficiency) and new (eccentricity and heterogeneity) measures of connectivity that incorporate link and nodal weights and auxiliary nodes. Nodal and link weights are introduced to take into account the importance of the components in the topology-based network model. Unweighted auxiliary nodes, locally refining the network model, allow one to capture the complexity of the connections between weighted end-nodes. The formulation presented in this paper is general and applicable to networks in different fields. The paper illustrates the implementation of the proposed formulation considering a transportation network subject to seismic excitation.