The Multiple Instances of Node Centrality and their Implications on the Vulnerability of ISP Networks

The position of the nodes within a network topology largely determines the level of their involvement in various networking functions. Yet numerous node centrality indices, proposed to quantify how central individual nodes are in this respect, yield very different views of their relative signi ficance. Our first contribution in this paper is then an exhaustive sur vey and categorization of centrality indices along several att ributes including the type of information (local vs. global) and processing complexity required for their computation. We next study the seven most popular of those indices in the context of Internet vulnerability to address issues that remain under-explored in literature so far. First, we carry out a correlation study to assess the consistency of the node rankings those indices generate over ISP router-level topologies. For each pair of indices, we compute the full ranking correlation, which is the standard choice in literature, and the percentage overlap between the k top nodes. Then, we let these rankings guide the removal of highly central nodes and assess the impact on both the connectivity properties and traffic-carrying capacity of the network. Our results confirm that the top- k overlap predicts the comparative impact of indices on the network vulnerability better than the full-ranking correlation. Importantly, the locally computed degree centrality index approximates closely the global indices with the most dramatic impact on the traffic-carryin g ca- pacity; whereas, its approximative power in terms of connectivity is more topology-dependent. I. I NTRODUCTION networks addressing how the position and power of individual actors relate to their social interconnections and the way t hey interact with the rest of the network. Such sociological stu dies motivated the introduction of various sociological indice s, which sought to quantify the importance of nodes and their re- lationships. Bavela's work appears to be the first to have giv en a formal definition of node centrality in connected graphs as the sum of its own geodesics (shortest-path distances) to al l other nodes. This work triggered a large research thread and a huge number of publications in the area of centrality indices. Many of them proposed new indices (3) or adaptations of existing ones that expanded their applicability in a broader range of

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