MANAGING NETWORK RISK VIA CRITICAL NODE IDENTIFICATION

We consider methodologies for managing risk in a telecommunication net- work based on identification of the critical nodes. The objec tive is to identify a set of vertices with a specified cardinality whose deletion result s is maximum number of discon- nected components. This is referred to as the CRITICAL NODE PROBLEM, and finds ap- plication in epidemic control, telecommunications, and military tactical planning, among others. From a telecommunication perspective, the set of critical nodes helps determine which players should be removed from the network in the event of a virus outbreak. Con- versely, in order to maintain maximum global connectivity, it should be ensured that the critical nodes remain intact. In this chapter, we review the recent work in this area and examine formulations based on integer linear programming. In this chapter, we study two variants of the CRITICAL NODE PROBLEM. In general, the objective of the CRITICAL NODE PROBLEM (CNP) is to find a set of k nodes in a graph whose deletion results in the maximum network fragmentation. By this we mean, maximize the number of components in thek-vertex deleted subgraph. Studies carried out in this line include those by Bavelas (6) and Freeman (15) which emphasize node centrality and prestige, both of which are usually functions of a nodes degree. However, they lacked applications to problems which emphasized network fragmentation and connectivity. We can apply the CNP to the problem of jamming wired telecommunication networks by identifying the critical nodes and suppressing the communication on these nodes. This will result in the maximum number of disconnected components which are unable to communi- cate with each other. The CNP can also be applied to the study of covert terrorist networks , where a certain number of individuals have to be identified wh ose deletion would result in the maximum breakdown of communication between individuals in the network (24). Likewise in order to stop the spreading of a virus over a telecommunication network, one can identify the critical nodes of the graph and take them offl ine. The CNP also finds applications in network immunization (9, 34) wher e mass vaccina- tion is an expensive process and only a specific number of peop le, modeled as nodes of a graph, can be vaccinated. The immunized nodes cannot propagate the virus and the goal is to identify the individuals to be vaccinated in order to redu ce the overall transmissibility of the virus. There are several vaccination strategies in the l iterature (see e.g. (9, 34)) offering control of epidemic outbreaks; however, none of the proposed are optimal strategies. The vaccination strategies suggested emphasize the centrality of nodes as a major factor rather than critical nodes whose deletion will maximize disconnectivity of the graph. Deletion of central nodes may not guarantee a fragmentation of the network or even disconnectivity, in which case disease transmission cannot be prevented. Of course, owing to its dynamic stature, the relationships between people, represented by edges in the social network are transient and there is a constant rewiring between nodes, and alternate relationships could