Measuring cascade effects in interdependent networks by using effective graph resistance

Understanding the correlation between the underlie network structure and overlay cascade effects in the interdependent networks is one of major challenges in complex network studies. There are some existing metrics that can be used to measure the cascades. However, different metrics such as average node degree interpret different characteristic of network topological structure, especially less metrics have been identified to effectively measure the cascading performance in interdependent networks. In this paper, we propose to use a combined Laplacian matrix to model the interdependent networks and their interconnectivity, and then use its effective resistance metric as an indicator to its cascading behavior. Moreover, we have conducted extensive comparative studies among different metrics such as average node degree, and the proposed effective resistance. We have found that the effective resistance metric can describe more accurate and finer characteristics on topological structure of the interdependent networks than average node degree which is widely adapted by the existing research studies for measuring the cascading performance in interdependent networks

Towards a Realistic Model for Failure Propagation in Interdependent Networks

Modern networks are becoming increasingly interdependent. As a prominent example, the smart grid is an electrical grid controlled through a communications network, which in turn is powered by the electrical grid. Such interdependencies create new vulnerabilities and make these networks more susceptible to failures. In particular, failures can easily spread across these networks due to their interdependencies, possibly causing cascade effects with a devastating impact on their functionalities. In this paper we focus on the interdependence between the power grid and the communications network, and propose a novel realistic model, HINT (Heterogeneous Interdependent NeTworks), to study the evolution of cascading failures. Our model takes into account the heterogeneity of such networks as well as their complex interdependencies. We compare HINT with previously proposed models both on synthetic and real network topologies. Experimental results show that existing models oversimplify the failure evolution and network functionality requirements, resulting in severe underestimations of the cascading failures.Comment: 7 pages, 6 figures, to be published in conference proceedings of IEEE International Conference on Computing, Networking and Communications (ICNC 2016), Kauai, US

Assortativity Decreases the Robustness of Interdependent Networks

It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and hence system-wide disasters. A recent model shows how pairs of interdependent networks can exhibit an abrupt percolation transition as failures accumulate. We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the two interdependent networks significantly changes the critical density of failures that triggers the total disruption of the two-network system. Specifically, we find that the assortativity (i.e. the likelihood of nodes with similar degree to be connected) within a single network decreases the robustness of the entire system. The results of this study on the influence of assortativity may provide insights into ways of improving the robustness of network architecture, and thus enhances the level of protection of critical infrastructures

Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependency

Increased coupling between critical infrastructure networks, such as power and communication systems, will have important implications for the reliability and security of these systems. To understand the effects of power-communication coupling, several have studied interdependent network models and reported that increased coupling can increase system vulnerability. However, these results come from models that have substantially different mechanisms of cascading, relative to those found in actual power and communication networks. This paper reports on two sets of experiments that compare the network vulnerability implications resulting from simple topological models and models that more accurately capture the dynamics of cascading in power systems. First, we compare a simple model of topological contagion to a model of cascading in power systems and find that the power grid shows a much higher level of vulnerability, relative to the contagion model. Second, we compare a model of topological cascades in coupled networks to three different physics-based models of power grids coupled to communication networks. Again, the more accurate models suggest very different conclusions. In all but the most extreme case, the physics-based power grid models indicate that increased power-communication coupling decreases vulnerability. This is opposite from what one would conclude from the coupled topological model, in which zero coupling is optimal. Finally, an extreme case in which communication failures immediately cause grid failures, suggests that if systems are poorly designed, increased coupling can be harmful. Together these results suggest design strategies for reducing the risk of cascades in interdependent infrastructure systems

Cascading Failures in Interdependent Infrastructures: An Interdependent Markov-Chain Approach

Many critical infrastructures are interdependent networks in which the behavior of one network impacts those of the others. Despite the fact that interdependencies are essential for the operation of critical infrastructures, such interdependencies can negatively affect the reliability and fuel the cascade of failures within and across the networks. In this paper, a novel interdependent Markov-chain framework is proposed that enables capturing interdependencies between two critical infrastructures with the ultimate goal of predicting their resilience to cascading failures and characterizing the effects of interdependencies on system reliability. The framework is sufficiently general to model cascading failures in any interdependent networks; however, this paper focuses on the electric-cyber infrastructure as an example. Using this framework it is shown that interdependencies among reliable systems, i.e., systems with exponentially distributed failure sizes, can make the individually reliable systems behave unreliably as a whole with power-law failure-size distributions

Social contagions on interdependent lattice networks

Although an increasing amount of research is being done on the dynamical processes on interdependent spatial networks, knowledge of how interdependent spatial networks influence the dynamics of social contagion in them is sparse. Here we present a novel non-Markovian social contagion model on interdependent spatial networks composed of two identical two-dimensional lattices. We compare the dynamics of social contagion on networks with different fractions of dependency links and find that the density of final recovered nodes increases as the number of dependency links is increased. We use a finite-size analysis method to identify the type of phase transition in the giant connected components (GCC) of the final adopted nodes and find that as we increase the fraction of dependency links, the phase transition switches from second-order to first-order. In strong interdependent spatial networks with abundant dependency links, increasing the fraction of initial adopted nodes can induce the switch from a first-order to second-order phase transition associated with social contagion dynamics. In networks with a small number of dependency links, the phase transition remains second-order. In addition, both the second-order and first-order phase transition points can be decreased by increasing the fraction of dependency links or the number of initially-adopted nodes.This work was partially supported by National Natural Science Foundation of China (Grant Nos 61501358, 61673085), and the Fundamental Research Funds for the Central Universities. (61501358 - National Natural Science Foundation of China; 61673085 - National Natural Science Foundation of China; Fundamental Research Funds for the Central Universities)Published versio

Critical infrastructure, panarchies and the vulnerability paths of cascading disasters

Cascading effects and cascading disasters are emerging fields of scientific research. The widespread diffusion of functional networks increases the complexity of interdependent systems and their vulnerability to large-scale disruptions. Although in recent years studies of interconnections and chain effects have improved significantly, cascading phenomena are often associated with the ‘‘toppling domino metaphor’’, or with high-impact, low-probability events. This paper aimed to support a paradigm shift in the state of the art by proposing a new theoretical approach to cascading events in terms of their root causes and lack of predictability. By means of interdisciplinary theory building, we demonstrate how cascades reflect the ways in which panarchies collapse. We suggest that the vulnerability of critical infrastructure may orientate the progress of events in relation to society’s feedback loops, rather than merely being an effect of natural triggers. Our conclusions point to a paradigm shift in the preparedness phase that could include escalation points and social nodes, but that also reveals a brand new field of research for disaster scholars