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Register a new userCascading failures in spatially-embedded random networks
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Cascading failures constitute an important vulnerability of interconnected systems. Here we focus on the study of such failures on networks in which the connectivity of nodes is constrained by geographical distance. Specifically, we use random geometric graphs as representative examples of such spatial networks, and study the properties of cascading failures on them in the presence of distributed flow. The key finding of this study is that the process of cascading failures is non-self-averaging on spatial networks, and thus, aggregate inferences made from analyzing an ensemble of such networks lead to incorrect conclusions when applied to a single network, no matter how large the network is. We demonstrate that this lack of self-averaging disappears with the introduction of a small fraction of long-range links into the network. We simulate the well studied preemptive node removal strategy for cascade mitigation and show that it is largely ineffective in the case of spatial networks. We introduce an altruistic strategy designed to limit the loss of network nodes in the event of a cascade triggering failure and show that it performs better than the preemptive strategy. Finally, we consider a real-world spatial network viz. a European power transmission network and validate that our findings from the study of random geometric graphs are also borne out by simulations of cascading failures on the empirical network.
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Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method shows that scale-free networks are more robust against cascading overload failures than ErdH{o}s-Renyi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works which neglect the effect of fluctuations of loads.
Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems, and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behavior. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed.
We investigate the effect of a specific edge weighting scheme $sim (k_i k_j)^{beta}$ on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter $beta$ and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we show the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different control parameter $beta$, we find that network resilience to cascading overloads and network throughput is optimal for the same value of $beta$ over the range of node capacities and available bandwidth.
We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting insights regarding Gibrats law for the rates of city growth (by population size), in partial support of the findings in a recent analysis of real data [Rozenfeld et al., Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008)]. The model produces a nontrivial relation between city population and city population density and a superlinear relationship between social connectivity and city population, both of which seem quite in line with real data.
In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and to the fruitful application of powerful methods used in statistical physics. Many important characteristics of social or biological systems can be described by the study of their underlying structure of interactions. Hierarchy is one of these features that can be formulated in the language of networks. In this paper we present some (qualitative) analytic results on the hierarchical properties of random network models with zero correlations and also investigate, mainly numerically, the effects of different type of correlations. The behavior of hierarchy is different in the absence and the presence of the giant components. We show that the hierarchical structure can be drastically different if there are one-point correlations in the network. We also show numerical results suggesting that hierarchy does not change monotonously with the correlations and there is an optimal level of non-zero correlations maximizing the level of hierarchy.
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