Identification of Critical Nodes and Edges in a Network Based on Clustering

Abstract

Network structures present within themselves specific characterization of their topological structures and connectivity. The properties of a given network change significantly as failure of its nodes and edges takes place. The failure of a node and/or edge reinstates the properties for the entire network. This paper aims to identify critical nodes and edges, the failure of which brings maximum change in the network properties. Clustering has been applied in this study for the identification process. The methodology discussed in this article would be helpful in tracking multi-states which a network undergoes due to failure of its nodes and edges. The proposed methodology would provide a holistic view for criticality of nodes and edges at both local and global level for a network. An optimum maintenance plan could then be devised for the critical nodes and edges to provide the system with a robust and resilient network. The proposed approach could be applied in power grid transmission, supply chain management, transportation and communication networks, oil, gas, power and water distribution networks to ensure continuous information and commodity flow through the networks. The methodology has been demonstrated with a case study in water distribution network. By applying the methodology, top five critical nodes and edges have been identified for the water distribution system.