We propose an algorithm to locate the most critical nodes to network robustness. Such critical nodes may be thought of as those most related to the notion of network centrality. Our proposal relies only on a localized spectral analysis of a limited subnetwork centered at each node in the network. We also present a procedure allowing the navigation from any node towards a critical node following only local information computed by the proposed algorithm. Experimental results confirm the effectiveness of our proposal considering networks of different scales and topological characteristics.
Network robustness is an important property derived from the connectivity level that directly impacts network reliability. There are many studies investigating network robustness in general and methods to evaluate network connectivity level @cite_2 @cite_13 @cite_9 . Nevertheless, to the best of our knowledge, only a few recent works target the distributed evaluation and location of the most critical nodes to network robustness, thus assessing node centrality @cite_10 @cite_20 @cite_18 in a distributed way.
@cite_13 @cite_18 @cite_9 @cite_2 @cite_10 @cite_20
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The function and performance of networks rely on their robustness, defined as their ability to continue functioning in the face of damage (targeted attacks or random failures) to parts of the network. Prior research has proposed a variety of measures to quantify robustness and various manipulation strategies to alter it. In this paper, our contributions are twofold. First, we critically analyze various robustness measures and identify their strengths and weaknesses. Our analysis suggests natural connectivity, based on the weighted count of loops in a network, to be a reliable measure. Second, we propose the first principled manipulation algorithms that directly optimize this robustness measure, which lead to significant performance improvement over existing, ad-hoc heuristic solutions. Extensive experiments on real-world datasets demonstrate the effectiveness and scalability of our methods against a long list of competitor strategies. An analysis is conducted on the robustness of measures of centrality in the face of random error in the network data. We use random networks of varying sizes and densities and subject them (separately) to four kinds of random error in varying amounts. The types of error are edge deletion, node deletion, edge addition, and node addition. The results show that the accuracy of centrality measures declines smoothly and predictably with the amount of error. This suggests that, for random networks and random error, we shall be able to construct confidence intervals around centrality scores. In addition, centrality measures were highly similar in their response to error. Dense networks were the most robust in the face of all kinds of error except edge deletion. For edge deletion, sparse networks were more accurately measured. Abstract Robustness of networked systems against noise corruption and structural changes in an underlying network topology is a critical issue for a reliable performance. In this paper, we investigate this issue of robustness in networked systems both from structural and functional viewpoints. Structural robustness deals with the effect of changes in a graph structure due to link or edge failures, while functional robustness addresses how well a system behaves in the presence of noise. We discuss that both of these aspects are inter-related, and can be measured through a common graph invariant. A graph process is introduced where edges are added to an existing graph in a step-wise manner to maximize robustness. Moreover, a relationship between the symmetry of an underlying network structure and robustness is also discussed. We examine the robustness of networks under attack when the attacker sequentially selects from a number of different attack strategies, each of which removes one node from the network. Network robustness refers to the ability of a network to maintain functionality under attack, and the problem-dependent context implies a number of robustness measures exist. Thus, we analyze four measures: (1) entropy, (2) efficiency, (3) size of largest network component, and suggest to also utilize (4) pairwise connectivity. Six network centrality measures form the set of strategies at the disposal of the attacker. Our study examines the utility of greedy strategy selection versus random strategy selection for each attack, whereas previous studies focused on greedy selection but limited to only one attack strategy. Using a set of common complex network benchmark networks, in addition to real-world networks, we find that randomly selecting an attack strategy often performs well when the attack strategies are of high quality. We also examine defense against the attacks by adding k edges after each node attack and find that the greedy strategy is most useful in this context. We also observed that a betweenness-based attack often outperforms both random and greedy strategy selection, the latter often becoming trapped in local optima.