Identification of K most vulnerable nodes in multi-layered network using a new model of interdependency

Abstract

The critical infrastructures of the nation including the power grid and the communication network are highly interdependent. Recognizing the need for a deeper understanding of the interdependency in a multi-layered network, significant efforts have been made by the research community in the last few years to achieve this goal. Accordingly a number of models have been proposed and analyzed. Unfortunately, most of the models are over simplified and, as such, they fail to capture the complex interdependency that exists between entities of the power grid and the communication networks involving a combination of conjunctive and disjunctive relations. To overcome the limitations of existing models, we propose a new model that is able to capture such complex interdependency relations. Utilizing this model, we provide techniques to identify the K most vulnerable nodes of an interdependent network. We show that the problem can be solved in polynomial time in some special cases, whereas for some others, the problem is NP-complete. We establish that this problem is equivalent to computation of a fixed point of a multilayered network system and we provide a technique for its computation utilizing Integer Linear Programming. Finally, we evaluate the efficacy of our technique using real data collected from the power grid and the communication network that span the Maricopa County of Arizona.

Modelling robustness of critical infrastructure networks

“…The fairness is the sum of the shortest paths from that particular node to all other nodes in the network. As the sum of the distances from all other nodes depends on number of nodes in the network, closeness centrality is normalised with n 1 [13].…”

“…It is the ratio of shortest path through a node or through an edge over the total number of shortest paths in that network. It is also a normalised value [13]. 4) Eigenvector Centrality: Eigenvector centrality is based on the concept that a node is important if it has richly connected neighbours.…”

Interdependencies modeling for the purpose of critical infrastructures protection

“…Implicative Interdependency Model [19] is an entity based Model that is able to capture complex dependency relationships existing between the entities of interdependent network systems. It uses Boolean Logic to model the interdependencies between networks entities, these interdependent relationships are termed as Implicative Interdependency Relations (IDRs) [19].…”

“…It uses Boolean Logic to model the interdependencies between networks entities, these interdependent relationships are termed as Implicative Interdependency Relations (IDRs) [19]. Interdependent network setting is represented as I(A,B,F(A,B)), where sets A={a 1 , a 2 , .., a n }and B={b 1 , b 2 ,.. b m } are the concerned networks entities, and F(A, B) is the set of dependency relations, or IDRs.…”

“…Table I represents a sample interdependent network I(A,B,F(A,B)), where A={a 1 ,a 2 , a 3 , a 4 }, B={b 1 , b 2 , b 3 } and F(A, B) is the set of IDRs between the entities of A and B. In this example, the IDR b 1 ← a 1 a 3 + a 2 implies that entity b 1 is operational if both entities a 1 and a 3 are operational, or entity a 2 is operational [19].…”