Robustness in response to unexpected events is always desirable for real-world networks. To improve the robustness of any networked system, it is important to analyze vulnerability to external perturbation such as random failures or adversarial attacks occurring to elements of the network. In this paper, we study an emerging problem in assessing the robustness of complex networks: the vulnerability of the clustering of the network to the failure of network elements. Specifically, we identify vertices whose failures will critically damage the network by degrading its clustering, evaluated through the average clustering coefficient. This problem is important because any significant change made to the clustering, resulting from element-wise failures, could degrade network performance such as the ability for information to propagate in a social network. We formulate this vulnerability analysis as an optimization problem, prove its NP-completeness and non-monotonicity, and we offer two algorithms to identify the vertices most important to clustering. Finally, we conduct comprehensive experiments in synthesized social networks generated by various well-known models as well as traces of real social networks. The empirical results over other competitive strategies show the efficacy of our proposed algorithms.
Vulnerability assessment has attracted a large amount of attention from the network science community. Work in the literature can be divided into two categories: Measuring the robustness and manipulating the robustness of a network. In measuring the robustness, different measures and metrics have been proposed such as the graph connectivity , the diameter, relative size of largest components, and average size of the isolated cluster . Other work suggests using the minimum node edge cut or the second smallest non-zero eigenvalue or the Laplacian matrix . In terms of manipulating the robustness, different strategies has been proposed such as , or using graph percolation . Other studies focus on excluding nodes by centrality measures, such as betweeness and the geodesic length , eigenvector , the shortest path between node pairs , or the total pair-wise connectivity . black @cite_0 @cite_1 developed integer programming frameworks to determine the critical nodes that minimize a connectivity metric subject to a budgetary constraint. For more information on network vulnerability assessments, the reader is referred to the surveys and and references therein.
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Assessing network vulnerability before potential disruptive events such as natural disasters or malicious attacks is vital for network planning and risk management. It enables us to seek and safeguard against most destructive scenarios in which the overall network connectivity falls dramatically. Existing vulnerability assessments mainly focus on investigating the inhomogeneous properties of graph elements, node degree for example, however, these measures and the corresponding heuristic solutions can provide neither an accurate evaluation over general network topologies, nor performance guarantees to large scale networks. To this end, in this paper, we investigate a measure called pairwise connectivity and formulate this vulnerability assessment problem as a new graph-theoretical optimization problem called &#946;-disruptor, which aims to discover the set of critical node edges, whose removal results in the maximum decline of the global pairwise connectivity. Our results consist of the NP-Completeness and inapproximability proof of this problem, an O(log n loglog n) pseudo-approximation algorithm for detecting the set of critical nodes and an O(log^1.5 n) pseudo-approximation algorithm for detecting the set of critical edges. In addition, we devise an efficient heuristic algorithm and validate the performance of the our model and algorithms through extensive simulations. We present a novel approach to quantify the vulnerability of a complex network, i.e., the capacity of a graph to maintain its functional performance under random damages or malicious attacks. The proposed measure represents a multiscale evaluation of vulnerability, and makes use of combined powers of the links’ betweenness. We show that the proposed approach is able to properly describe some cases for which earlier measures of vulnerability fail. The relevant applications of our method for technological network design are outlined. In this paper, we propose two metrics, i.e., the optimal repair time and the resilience reduction worth, to measure the criticality of the components of a network system from the perspective of their contribution to system resilience. Specifically, the two metrics quantify: 1) the priority with which a failed component should be repaired and re-installed into the network and 2) the potential loss in the optimal system resilience due to a time delay in the recovery of a failed component, respectively. Given the stochastic nature of disruptive events on infrastructure networks, a Monte Carlo-based method is proposed to generate probability distributions of the two metrics for all of the components of the network; then, a stochastic ranking approach based on the Copeland's pairwise aggregation is used to rank components importance. Numerical results are obtained for the IEEE 30-bus test network and a comparison is made with three classical centrality measures. In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the cross-over from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Pade approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model. Appears in Phys. Rev. E 60, 7332-7342 (1999).