In this article we present the Hayastan Shakarian (HS), a robustness index for complex networks. HS measures the impact of a network disconnection (edge) while comparing the sizes of the remaining connected components. Strictly speaking, the Hayastan Shakarian index is defined as edge removal that produces the maximal 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 using the Hayastan Shakarian cut (disconnecting the edge with max HS) and other well-known strategies as the higher betweenness centrality disconnection. All strategies 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 using the Hayastan Shakarian cut are more dangerous (decreasing the robustness) than the same attacks based on other centrality measures. We believe that the Hayastan Shakarian cut, 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 captured the attention of researchers and practitioners nowadays. For instance, @cite_11 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 100+ @math 0 In the study of resilience after edge removing, @cite_13 study backup communication paths for network services defining that a network is '' given that ''.
@cite_13 @cite_11
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Centrality measures are widely used to identify leaders of covert networks. We study how a group of such leaders can avoid being detected by such measures. More concretely, we study the hardness of choosing a set of edges that can be added to the network in order to decrease the leaders' ranking according to two fundamental centrality measures, namely degree, and closeness. We prove that this problem is NP-complete for each measure. We then study how the leaders can construct a network from scratch, designed specifically for them to hide in disguise. We identify a network structure that not only guarantees to hide the leaders to a certain extent, but also allows them to spread their influence across the network. Simulation studies using susceptible-infectious-recovered models were conducted to estimate individuals’ risk of infection and time to infection in small-world and randomly mixing networks. Infection transmitted more rapidly but ultimately resulted in fewer infected individuals in the small-world, compared with the random, network. The ability of measures of network centrality to identify high-risk individuals was also assessed. ‘‘Centrality’’ describes an individual’s position in a population; numerous parameters are available to assess this attribute. Here, the authors use the centrality measures degree (number of contacts), random-walk betweenness (a measure of the proportion of times an individual lies on the path between other individuals), shortest-path betweenness (the proportion of times an individual lies on the shortest path between other individuals), and farness (the sum of the number of steps between an individual and all other individuals). Each was associated with time to infection and risk of infection in the simulated outbreaks. In the networks examined, degree (which is the most readily measured) was at least as good as other network parameters in predicting risk of infection. Identification of more central individuals in populations may be used to inform surveillance and infection control strategies. A complex network can be modeled as a graph representing the ''who knows who'' relationship. In the context of graph theory for social networks, the notion of centrality is used to assess the relative importance of nodes in a given network topology. For example, in a network composed of large dense clusters connected through only a few links, the nodes involved in those links are particularly critical as far as the network survivability is concerned. This may also impact any application running on top of it. Such information can be exploited for various topological maintenance issues to prevent congestion and disruption. This can also be used offline to identify the most important actors in large social interaction graphs. Several forms of centrality have been proposed so far. Yet, they suffer from imperfections: initially designed for small social graphs, they are either of limited use (degree centrality), either incompatible in a distributed setting (e.g. random walk betweenness centrality). In this paper we introduce a novel form of centrality: the second order centrality which can be computed in a distributed manner. This provides locally each node with a value reflecting its relative criticity and relies on a random walk visiting the network in an unbiased fashion. To this end, each node records the time elapsed between visits of that random walk (called return time in the sequel) and computes the standard deviation (or second order moment) of such return times. The key point is that central nodes see regularly the random walk compared to other topology nodes. Both through theoretical analysis and simulation, we show that the standard deviation can be used to accurately identify critical nodes as well as to globally characterize graphs topology in a distributed way. We finally compare our proposal to well-known centralities to assess its competitivity. We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph. For each case of attacks on vertices and edges, four different attacking strategies are used: removals by the descending order of the degree and the betweenness centrality, calculated for either the initial network or the current network during the removal procedure. It is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network, suggesting that the network structure changes as important vertices or edges are removed. Furthermore, the correlation between the betweenness centrality and the degree in complex networks is studied.