In this article we present Miuz, a robustness index for complex networks. Miuz measures the impact of disconnecting a node from the network while comparing the sizes of the remaining connected components. Strictly speaking, Miuz for a node is defined as the inverse of the size of the largest connected component divided by the sum of the sizes of the remaining ones. We tested our index in attack strategies where the nodes are disconnected in decreasing order of a specified metric. We considered Miuz and other well-known centrality measures such as betweenness, degree, and harmonic centrality. All of these metrics were compared regarding the behavior of the robustness (R- index) during the attacks. In an attempt to simulate the internet backbone, the attacks were performed in complex networks with power-law degree distributions (scale-free networks). Preliminary results show that attacks based on disconnecting a few number of nodes Miuz are more dangerous (decreasing the robustness) than the same attacks based on other centrality measures. We believe that Miuz, as well as other measures based on the size of the largest connected component, provides a good addition to other robustness metrics for complex networks.
The idea of planning a network attack'' using centrality measures has been catching the attention of researchers and practitioners nowadays. For instance, @cite_5 used bet -ween -ness-centrality () for planning a network attack, calculating the value for all nodes, ordering nodes from higher to lower , and then attacking (discarding) those nodes in that order. They have shown that disconnecting only two of the top -ranked nodes , their packet-delivery ratio is reduced to @math 10 @math 0 Concerning centrality measures, betweenness centrality deserves special attention. Betweenness has been studied as a resilience metric for the routing layer @cite_6 and also as a robustness metric for complex networks @cite_11 and for internet autonomous systems networks @cite_4 among others.
@cite_5 @cite_4 @cite_6 @cite_11
2014770087 2139905147 2142843434 2024982571
As the Internet becomes increasingly important to all aspects of society, the consequences of disruption become increasingly severe. Thus it is critical to increase the resilience and survivability of the future network. We define resilience as the ability of the network to provide desired service even when challenged by attacks, large-scale disasters, and other failures. This paper describes a comprehensive methodology to evaluate network resilience using a combination of analytical and simulation techniques with the goal of improving the resilience and survivability of the Future Internet. We calculate an extensive set of characteristics for Internet AS topologies extracted from the three data sources most frequently used by the research community: traceroutes, BGP, and WHOIS. We discover that traceroute and BGP topologies are similar to one another but differ substantially from the WHOIS topology. Among the widely considered metrics, we find that the joint degree distribution appears to fundamentally characterize Internet AS topologies as well as narrowly define values for other important metrics. We discuss the interplay between the specifics of the three data collection mechanisms and the resulting topology views. In particular, we how how the data collection peculiarities explain differences in the resulting joint degree distributions of the respective topologies. Finally, we release to the community the input topology datasets, along with the scripts and output of our calculations. This supplement hould enable researchers to validate their models against real data and to make more informed election of topology data sources for their specific needs The cost of failures within communication networks is significant and will only increase as their reach further extends into the way our society functions. Some aspects of network resilience, such as the application of fault-tolerant systems techniques to optical switching, have been studied and applied to great effect. However, networks - and the Internet in particular - are still vulnerable to malicious attacks, human mistakes such as misconfigurations, and a range of environmental challenges. We argue that this is, in part, due to a lack of a holistic view of the resilience problem, leading to inappropriate and difficult-to-manage solutions. In this article, we present a systematic approach to building resilient networked systems. We first study fundamental elements at the framework level such as metrics, policies, and information sensing mechanisms. Their understanding drives the design of a distributed multilevel architecture that lets the network defend itself against, detect, and dynamically respond to challenges. We then use a concrete case study to show how the framework and mechanisms we have developed can be applied to enhance resilience. Many complex systems can be described by networks, in which the constituent components are represented by vertices and the connections between the components are represented by edges between the corresponding vertices. A fundamental issue concerning complex networked systems is the robustness of the overall system to the failure of its constituent parts. Since the degree to which a networked system continues to function, as its component parts are degraded, typically depends on the integrity of the underlying network, the question of system robustness can be addressed by analyzing how the network structure changes as vertices are removed. Previous work has considered how the structure of complex networks change as vertices are removed uniformly at random, in decreasing order of their degree, or in decreasing order of their betweenness centrality. Here we extend these studies by investigating the effect on network structure of targeting vertices for removal based on a wider range of non-local measures of potential importance than simply degree or betweenness. We consider the effect of such targeted vertex removal on model networks with different degree distributions, clustering coefficients and assortativity coefficients, and for a variety of empirical networks.