The scattering number of a graph G, denoted sc(G), is defined by sc(G)=max{c(G−S)− |S| : S ⊆ V(G) and c(G−S)≠ 1} where c(G−S) denotes the number of components in G− S. It is one measure of graph vulnerability. In this paper, general results on the scattering number of a graph are considered. Firstly, some bounds on the scattering number are given. Further, scattering number of a binomial tree i...

During major power system disturbances, when multiple component outages occur in rapid succession, it becomes crucial to quickly identify the transmission interconnections that have limited transfer capability. Understanding impact of an outage on these critical (called saturated cut-sets) is important for enhancing situational awareness and taking correct actions. This paper proposes a new gra...

This report presents a graph-based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The analysis system requires as input a database of common attacks, broken into atomic steps,...

We present a novel approach to quantify the vulnerability of a complex network, i.e., the capacity of a graph to maintain its functional performance under random damages or malicious attacks. The proposed measure represents a multiscale evaluation of vulnerability, and makes use of combined powers of the links' betweenness. We show that the proposed approach is able to properly describe some ca...

Many critical infrastructures consist of networks with complex structure, since they have highly interdependent elements and nontrivial designs with a degree of complexity that depends on the settings and level of interaction between these elements. The theory of complex networks employs techniques borrowed from graph theory to classify different types of networks, analyse their structures, and...

The scattering number is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the neighbour isolated version of the parameter. The neighbour isolated scattering number of a noncomplete graph G is defined to be NIS(G) =max{i(G/X )−|X | : i(G/X )3⁄4 1} where the maximum is taken over all X , the cut strategy of G, and i(G/X ) is the number of componen...

This paper presents aCAT Advanced Cellular Network Vulnerability Assessment Toolkit, a graph based end-to-end vulnerability assessment tool for 3G networks. The novelties of this tool include (1) usage of technical specifications written in the Specification and Description Language (SDL); (2) the definition of a network dependency model for accurate chain derivation; and (3) exhaustive attack ...

Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of networks. We establish an unexpected connection between network vulnerability and graph regularizability. We use the Shapley value of coalition games to introduce...

A general method for the computation of various parameters measuring the vulnerability of a graph is introduced. Four measures of vulnerability are considered, i.e., the toughness, scattering number, vertex integrity and the size of a minimum balanced separator. We show how to compute these parameters by polynomial time algorithms for various classes of intersection graphs like permutation grap...

The tenacity of an incomplete connected graph G is defined as T (G) = min{ |S|+m(G−S) ω(G−S) : S ⊂ V (G), ω(G− S) > 1}, where ω(G− S) and m(G− S), respectively, denote the number of components and the order of a largest component inG−S. This is a reasonable parameter to measure the vulnerability of networks, as it takes into account both the amount of work done to damage the network and how bad...