[Paper Review] The Multiple Instances of Node Centrality and their Implications on the Vulnerability of ISP Networks

George G. Nomikos, Panagiotis Pantazopoulos+2 more|arXiv (Cornell University)|Dec 17, 2013

Graph theory and applications4 citations

TL;DR

This paper investigates the impact of different node centrality indices on Internet Service Provider (ISP) network vulnerability by analyzing their rankings across 40+ router-level topologies. It finds that top-k overlap in centrality rankings, not full-ranking correlation, better predicts network degradation; remarkably, degree centrality—computed locally—closely approximates the worst-case impact on traffic capacity.

ABSTRACT

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 significance. Our first contribution in this paper is then an exhaustive survey and categorization of centrality indices along several attributes 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-carrying capacity; whereas, its approximative power in terms of connectivity is more topology-dependent.

Motivation & Objective

• To systematically classify and survey over 30 node centrality indices proposed in the last 60 years across sociological, physical, and computational disciplines.
• To assess the consistency and reliability of seven widely used centrality indices—degree, betweenness, eigenvector, closeness, PageRank, and others—in ranking nodes within real ISP router-level topologies.
• To evaluate how effectively different centrality indices predict network vulnerability when used to guide targeted node removals, focusing on both connectivity and traffic-carrying capacity.
• To challenge the conventional use of full-ranking correlation as a proxy for index equivalence, proposing top-k overlap as a more accurate predictor of network impact.

Proposed method

• Developed a novel classification scheme for node centrality indices based on attributes such as information type (local vs. global), computational complexity, and underlying graph-theoretic principles.
• Collected and analyzed 40+ router-level ISP network snapshots across multiple years to derive node rankings using seven representative centrality indices: degree, betweenness, eigenvector, closeness, PageRank, and two others.
• Computed standard rank correlation (e.g., Spearman’s rho) and introduced a new metric—percentage overlap in the top-k most central nodes—to assess ranking similarity.
• Simulated targeted node removals guided by each centrality index and measured the resulting impact on network connectivity (e.g., number of connected components, inverse geodesic length) and traffic-carrying capacity.
• Used statistical analysis to compare the predictive power of full-ranking correlation versus top-k overlap in forecasting network degradation under different attack strategies.

Experimental results

Research questions

• RQ1 How consistent are the node rankings produced by different centrality indices across real ISP router-level topologies?
• RQ2 To what extent does full-ranking correlation between centrality indices reflect their actual impact on network vulnerability?
• RQ3 Does the top-k overlap in centrality rankings better predict the comparative impact of different indices on network resilience than full-ranking correlation?
• RQ4 Can a locally computable centrality index (e.g., degree centrality) approximate the impact of globally computed indices on network performance metrics like traffic capacity?
• RQ5 What is the effect of combining rankings from multiple centrality indices on the severity of network degradation due to targeted attacks?

Key findings

• Full-ranking correlation between centrality indices is often high, but this correlation is significantly inflated by agreement on poorly ranked nodes (e.g., degree=1, betweenness=0), weakening its predictive power for top-tier nodes.
• The percentage overlap in the top-5% most central nodes (top-k overlap) is a far more accurate predictor of similar network degradation impact than full-ranking correlation.
• Degree centrality, computed using only local information, closely approximates the worst-case impact on network traffic-carrying capacity, despite being a local metric.
• The impact of node removals guided by different centrality indices varies significantly across topologies and performance metrics, with no single index universally dominating.
• Eigenvector centrality consistently induces the least impact on network resilience, while indices like betweenness and PageRank show more dramatic effects depending on topology and metric.
• Mixing rankings from a local index (e.g., degree) and a global one (e.g., betweenness) can yield more damaging attack sets when their top-k overlap is low, suggesting a strategic advantage in hybrid targeting.