Cascade-robustness optimization of coupling preference in interconnected networks

Cascading failures in interconnected networks with dynamical redistribution of loads

In network security, how to use efficient response methods against cascading failures of complex networks is very important. In this paper, concerned with the highest-load attack (HL) and random attack (RA) on one edge, we define five kinds of weighting strategies to assign the external resources for recovering the edges from cascading failures in heterogeneous scale-free (SF) networks. The influence of external resources, the tolerance parameter, and the different weighting strategies on SF networks against cascading failures is investigated carefully. We find that, under HL attack, the fourth kind of weighting method can more effectively improve the integral robustness of SF networks, simultaneously control the spreading velocity, and control the outburst of cascading failures in SF networks than other methods. Moreover, the third method is optimal if we only knew the local structure of SF networks and the uniform assignment is the worst. The simulations of the real-world autonomous system in, Internet have also supported our findings. The results are useful for using efficient response strategy against the emergent accidents and controlling the cascading failures in the real-world networks.

A memetic algorithm for enhancing the robustness of scale-free networks against malicious attacks

Many infrastructure networks, such as power grids, road networks, and the Internet, are embedded in space. These networks are extremely susceptible to geographically localized attacks caused by natural disasters and will experience cascading overload failures due to node load redistribution. Analyzing the robustness of these spatial networks under extreme geographically localized attacks (EGLAs), in which attacks target the most critical locations of networks, is important for improving their safety. However, existing studies for analyzing the robustness of spatial networks under EGLA only consider the initial failures caused by attacks, ignoring the effect of cascading overload failures. In this paper, we simultaneously consider the effects of the above factors to study the robustness of networks with loads under EGLA. We construct a strategy to identify the locations of the EGLA by maximizing the importance of nodes in the attack regions and propose an adaptive simulated annealing algorithm to solve it. Experiments in the synthetic and real-world networks show that our strategy can find the locations of attacks more accurately compared to traditional methods. Remarkably, we find that the link length distribution of the network can affect the robustness of the network by influencing the betweenness distribution of the nodes. Accordingly, a strategy by randomly adding long-range edges is designed to improve the robustness of real infrastructure networks, which can provide new insights into the safety of systems.

When designing a transport network, decisions are made according to an expected value for network state variables, such as infrastructure and vehicle conditions, which are uncertain at a planning horizon of up to decades. Because disruptions, such as infrastructure breakdowns, will arise and affect the network on the day of operations, actions must be taken from the network design. Robust network designs may be implemented but they are extremely expensive if disruptions do not realise. In this paper, we propose a novel approach to the network design problem where robustness and recovery are combined. We look for the trade-off between efficiency and robustness accounting for the possibility of recovering from disruptions: recoverable robust network design. Computational experiments drawn from fictitious and realistic networks show how the presented approach reduces the price of robustness and recovery costs as compared to traditional robust and non-robust rapid transit network design approaches.

The robustness of infrastructure networks has attracted great attention in recent years. Scholars have studied the robustness of complex networks against cascading failures from different aspects. In this paper, a new capacity allocation strategy is proposed to reduce cascading failures and improve network robustness without changing the network structure. Compared with the typical strategy proposed in Motter–Lai (ML) model, the new strategy can reduce the scale of cascading failure. The new strategy applied in scale-free network is more efficient. In addition, to reasonably evaluate the two strategies, we introduce contribution rate of unit capacity to network robustness as evaluation index. Results show that our new strategy works well, and it is more advantageous in the rational utilization of capacity in scale-free networks. Furthermore, we were surprised to find that the efficient utilization of capacity costs declined as costs rose above a certain threshold, which indicates that it is not wise to restrain cascading failures by increasing capacity costs indefinitely.

The robustness of complex networks against cascading failures has been of great interest, while most of the researchers have considered undirected networks. However, to be more realistic, a part of links of many real systems should be described as unidirectional. In this paper, by applying three link direction-determining (DD) strategies, the tolerance of cascading failures is investigated in various networks with both unidirectional and bidirectional links. By extending the utilization of a classical global betweenness method, we propose a new cascading model, taking into account the weights of nodes and the directions of links. Then, the effects of unidirectional links on the network robustness against cascaded attacks are examined under the global load-based distribution mechanism. The simulation results show that the link-directed methods could not always lead to the decrease of the network robustness as indicated in the previous studies. For small-world networks, these methods certainly make the network weaker. However, for scale-free networks, the network robustness can be significantly improved by the link-directed method, especially for the method with non-random DD strategies. These results are independent of the weight parameter of the nodes. Due to the strongly improved robustness and easy realization with low cost on networks, the method for enforcing proper links to the unidirectional ones may be useful for leading to insights into the control of cascading failures in real-world networks, like communication and transportation networks.

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 show that scale-free networks are more robust against cascading overload failures than Erdős-Rényi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works, which neglect the effect of fluctuations of loads.

Interconnection networks are commonly modeled as graphs, where vertices represent processors or devices and edges represent communication links. In such networks, locating or identifying components using a small set of reference points is fundamental for routing, fault diagnosis, monitoring, and navigation. A standard graph-theoretic measure of this capability is the metric dimension (or locating number), defined as the minimum cardinality of a resolving set whose distance vectors uniquely distinguish all vertices. Since determining the metric dimension is NP-hard in general, exact values for structured network families are of both theoretical and practical interest. In this paper, we studied the metric dimension of the line graph of an optimal $ 2 $-fault-tolerant token ring network. The underlying network $ \mathbb{T}_{m}^{2} $ augments a simple ring with additional links to ensure robust connectivity under up to two link or node failures, while the line graph $ L(\mathbb{T}_{m}^{2}) $ represents the network at the link level. A lemma was established to prove the lower bound of the metric dimension via contradiction, while the upper bound was determined by explicitly constructing resolving sets. The analysis was conducted case by case according to the congruence of the network order modulo $ 4 $, which simplified verification of all representation vectors. Our results showed that the fault-tolerant links increase the metric dimension compared with ordinary token rings, highlighting the influence of additional links on network distinguishability and providing insights for the design of robust interconnection networks.

Cascading failures of loads in isolated networks under random failures or intentional attacks have been studied in the past decade. The corresponding results for interconnected networks remain missing. In this paper we extend the cascading failure model used in isolated networks to the case of interconnected networks, and study cascades of failures in a data-packet transport scenario. We find that for sparse coupling, enhancing the coupling probability can make interconnected networks more robust against intentional attacks, but keeping increasing the coupling probability has the opposite effect for dense coupling. Additionally, the optimal coupling probability is largely affected by the coupling preference. Finally, assortative coupling is more helpful to resist the cascades compared to disassortative or random coupling. These results can be useful for the design and optimization of interconnected networks such as communication networks, power grids and transportation systems.

Research on cascading failure in multilayer network with different coupling preference

An efficient local cascade defense method in complex networks

Power grids are closely related to people's daily life, and cascading failure plays a vital role in their reliability, which has attracted intensive research interests in the past few years. Numerous researches concerning cascading failure in dynamic power grids, still, most of them focus on the prediction of cascading failure and recovery after failure while Time-of-Arrival (TOA) of cascading failure is rarely concerned. The TOA -based prediction of cascading failure often needs to consider the entire cascading process of the target network during the entire cascading failure process, which brings great loss in network reliability and computational overhead. In light of this, we propose a prediction model of cascading failure based on TOA to implement the prediction of cascading failure in dynamic power grids. We successfully perform our model on two artificial synthetic networks and one real-world network by comparing against four widely used prediction models. We further analyze the non-negligible superiority of our scheme overall benchmarks. As far as we know, we are the first to introduce the conception of TOA for cascading failure prediction in the dynamic power grids.

Robustness of supply chain networks against underload cascading failures

Core infrastructure systems like water, electricity, transport, and communication are fundamental to modern cities, supporting vital services and everyday societal operations. However, their resilience is increasingly threatened by the occurrence and severity of compound hazards, such as floods that occurs concurrently with power system outages. These risks increase systemic risks that go far beyond the original source of disruption and frequently cause cascade failures throughout interconnected networks. With an emphasis on the dynamics of interdependencies and cascading consequences, this study investigates the resilience of urban lifeline networks under compound hazard situations. To capture the multi-layered vulnerabilities of lifeline systems, the study combines functional dependencies, performance indicators, and hazard scenarios using a network-based modelling technique. The results demonstrate how interruptions in one industry may quickly spread to others, worsening service outages and impairing emergency response capabilities. Key resilience measures—robustness, redundancy, and recovery time—are evaluated to identify vulnerable nodes and routes under compound hazards. The paper also explores mitigation strategies such as advanced monitoring, decentralized energy systems, and adaptive infrastructure design. By linking hazard modelling with resilience assessment, the study advances knowledge and offers practical insights for policymakers and engineers to strengthen urban lifeline resilience. This review uniquely synthesizes recent advances in understanding the interdependencies and cascading dynamics of urban lifeline systems exposed to compound hazards. It provides a comprehensive framework that integrates systemic risk concepts with resilience assessment approaches, offering new insights for urban resilience research and practice. This review contributes to the current body of knowledge by synthesizing existing research on cascading failures and systemic risks affecting urban lifeline systems under compound hazards, and by proposing a conceptual framework to enhance urban resilience planning and risk-informed decision-making.