**Revisiting Models of Vulnerabilities of the Networks **

**Horia-Nicolai L. TEODORESCU ^{1,2 } **

**Romanian Academy, Iasi Branch,**

^{1 }Bd. Carol I nr. 8, Iasi, Romania

hteodor@etti.tuiasi.ro

**“Gheorghe Asachi” Technical University of Iasi Romania,**

^{2}Str. D. Mangeron 64, Iasi, Romania

**Abstract: **The study critically revisits the models of ‘vulnerability’ of various types of networks and shows several limits of the current state of the art, including the ambiguous definitions of vulnerability and robustness concepts, the arbitrary use of various connectivity indexes on graphs for assessing the ‘vulnerability’ of real-world networks to real-world attacks, the lack of any evidence for the proposed models, and the lack of significant statistical approaches. Next, the study shows the limits of using the world ‘measure’ and ‘metric’ in relation with connectivity characteristics on graphs. Then, a general cause-effect chain for attacks on networks, especially computer and transportation networks is laid down as a basis for probabilistic model building. Evidence is provided on the relation between graph features and the probabilities of events under an attack and model examples are discussed. An annex on the caution of making public detailed knowledge on such models ends the paper.

**Keywords:** networks, attacks, risk, connectivity indexes, network vulnerability, probabilistic model, evidence.

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**CITE THIS PAPER AS**:

Horia-Nicolai L. TEODORESCU, **Revisiting Models of Vulnerabilities of the Networks**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 25(4), pp. 469-478, 2016.

**Introduction
**

For more than four decades, the issues of the reliability and vulnerability to attacks were studied for computer and communication networks (CCN), mainly using graph models and tools [4], [5], [25], [29]. More recently, similar tools have been applied to transportation systems in relation with several infamous attacks in various countries [8], [19]. A large number of studies have been recently devoted to the vulnerability of transportation networks [19], especially of subways [7], [9-11], [32], [33] due to several attacks on them. Many of these studies focused on the vulnerability of nodes and edges of the networks, in relation with the network topology, and proposed indexes of vulnerability, sometimes weighted by flows; in this way, the models for computer networks were directly transposed to transportation ones, without discussing the foundation of the model extension from one type of networks to another. These studies have no evidence support and remain largely disconnected from the real life situations; moreover, many of these studies use intuitive yet qualitative and vague meanings for features such as vulnerability, robustness, and resilience.

We critically revisit some of the concepts and issues related to ‘vulnerability’ and concerning specifically transportation networks; new network indexes are proposed that have the potential of being more suitable (Section 4). Next, probabilistic models are suggested for the attacks and for computing the outcome in probabilistic terms for attacks, depending on the node properties (Sections 3-5).

The first set of contributions of this study is theoretical; in obtaining them, the method applied is based on graph analysis and probabilistic approach; tentative speculative models are proposed (Sections 3-5). A second core contribution consists in binging evidence for the derivation of models for key probabilities involved in the analysis; examples are presented and references to actual transportation networks are made in Section 6. The remaining part of this introductory section is devoted to the terminology related to graph features and to the general concept of vulnerability.

The organization of the paper is largely linear; Section 2 reviews some graph models related to vulnerability of networks, while Section 3 and 4 clarify aspects related to chains of effects and the related probabilities. Section 5 details the role of nodes and edges in the attack probability of networks. A model based on seemingly natural assumption is built in Section 6 and its predictions are contrasted in Section 7 with the evidence-based models for attack probability. The last section contains conclusions.

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