On network criticality in robustness analysis of a network structure

On network criticality in robustness analysis of a network structure

**Authors : **

A. Bharali ^{1 *} and Dimpee Baruah ^{2}

**Author Address : **

^{1,2} Department of Mathematics, Dibrugarh University, Dibrugarh-786004, India.

*Corresponding author.

**Abstract : **

Robustness of a network is the ability of the network to maintain its functionality when some vertices or edges are removed due to targeted attacks or random failures. This paper studies an interesting graph measure that we call the network criticality. The notion of network criticality is derived from the probabilistic definition of betweenness, which is defined based on random walks in a graph, as the main metric to quantify the survival value of a network with respect to changes in topology and dynamics. The objective of the paper is twofold. First, we discuss some known formulae of network criticality and derive its relation with some other graph measures. Second, we propose a new measure of network functionality based on network criticality.

**Keywords : **

Robustness, Network criticality, Graph measures.

**DOI : **

**Article Info : **

*Received : * December 19, 2018; *Accepted : * March 16, 2019.