Mitigation of cascading failures in complex networks

Optimizing the robustness of higher-low order coupled networks

Enhancing the robustness of complex networks is of great practical significance as it ensures the stable operation of infrastructure systems. We measure its robustness by examining the size of the largest connected component of the network after initial attacks. However, traditional research on network robustness enhancement has mainly focused on low-order networks, with little attention given to higher-order networks, particularly higher-low order coupling networks(the largest connected component of the network must exist in both higher-order and low-order networks). To address this issue, this paper proposes robust optimization methods for higher-low order coupled networks based on the greedy algorithm and the simulated annealing algorithm. By comparison, we found that the simulated annealing algorithm performs better. The proposed method optimizes the topology of the low-order network and the higher-order network by randomly reconnecting the edges, thereby enhancing the robustness of the higher-order and low-order coupled network. The experiments were conducted on multiple real networks to evaluate the change in the robustness coefficient before and after network optimization. The results demonstrate that the proposed method can effectively improve the robustness of both low-order and higher-order networks, ultimately enhancing the robustness of higher-low order coupled networks.

Improving Robustness of High-Low-Order Coupled Networks against Malicious Attacks Based on a Simulated Annealing Algorithm

Malicious attacks can cause significant damage to the structure and functionality of complex networks. Previous research has pointed out that the ability of networks to withstand malicious attacks becomes weaker when networks are coupled. However, traditional research on improving the robustness of networks has focused on individual low-order or higher-order networks, lacking studies on coupled networks with higher-order and low-order networks. This paper proposes a method for optimizing the robustness of coupled networks with higher-order and low-order based on a simulated annealing algorithm to address this issue. Without altering the network's degree distribution, the method rewires the edges, taking the robustness of low-order and higher-order networks as joint optimization objectives. Making minimal changes to the network, the method effectively enhances the robustness of coupled networks. Experiments were conducted on Erdős-Rényi random networks (ER), scale-free networks (BA), and small-world networks (SW). Finally, validation was performed on various real networks. The results indicate that this method can effectively enhance the robustness of coupled networks with higher-order and low-order.

Predicting the cascading dynamics in complex networks via the bimodal failure size distribution

Cascading failure as a systematic risk occurs in a wide range of real-world networks. Cascade size distribution is a basic and crucial characteristic of systemic cascade behaviors. Recent research works have revealed that the distribution of cascade sizes is a bimodal form indicating the existence of either very small cascades or large ones. In this paper, we aim to understand the properties and formation characteristics of such bimodal distribution in complex networks and further predict the final cascade size. We first find that the bimodal distribution is ubiquitous under certain conditions in both synthetic and real networks. Moreover, the large cascades distributed in the right peak of bimodal distribution are resulted from either the failure of nodes with high load at the first step of the cascade or multiple rounds of cascades triggered by the initial failure. Accordingly, we propose a hybrid load metric (HLM), which combines the load of the initial broken node and the load of failed nodes triggered by the initial failure, to predict the final size of cascading failures. We validate the effectiveness of HLM by computing the accuracy of identifying the cascades belonging to the right and left peaks of the bimodal distribution. The results show that HLM is a better predictor than commonly used network centrality metrics in both synthetic and real-world networks. Finally, the influence of network structure on the optimal HLM is discussed.

Fragility Induced by Interdependency of Complex Networks and Their Higher-Order Networks

The higher-order structure of networks is a hot research topic in complex networks. It has received much attention because it is closely related to the functionality of networks, such as network transportation and propagation. For instance, recent studies have revealed that studying higher-order networks can explore hub structures in transportation networks and information dissemination units in neuronal networks. Therefore, the destruction of the connectivity of higher-order networks will cause significant damage to network functionalities. Meanwhile, previous works pointed out that the function of a complex network depends on the giant component of the original(low-order) network. Therefore, the network functionality will be influenced by both the low-order and its corresponding higher-order network. To study this issue, we build a network model of the interdependence of low-order and higher-order networks (we call it ILH). When some low-order network nodes fail, the low-order network's giant component shrinks, leading to changes in the structure of the higher-order network, which further affects the low-order network. This process occurs iteratively; the propagation of the failure can lead to an eventual network crash. We conducted experiments on different networks based on the percolation theory, and our network percolation results demonstrated a first-order phase transition feature. In particular, we found that an ILH is more fragile than the low-order network alone, and an ILH is more likely to be corrupted in the event of a random node failure.

Three Decades in Econophysics—From Microscopic Modelling to Macroscopic Complexity and Back

We explore recent contributions to research in Econophysics, switching between Macroscopic complexity and microscopic modelling, showing how each leads to the other and detailing the everyday applicability of both approaches and the tools they help develop. Over the past decades, the world underwent several major crises, leading to significant increase in interdependence and, thus, complexity. We show here that from the perspective of network science, these processes become more understandable and, to some extent, also controllable.

Effects of mobility restrictions during COVID19 in Italy

To reduce the spread and the effect of the COVID-19 global pandemic, non-pharmaceutical interventions have been adopted on multiple occasions by governments. In particular lockdown policies, i.e., generalized mobility restrictions, have been employed to fight the first wave of the pandemic. We analyze data reflecting mobility levels over time in Italy before, during and after the national lockdown, in order to assess some direct and indirect effects. By applying methodologies based on percolation and network science approaches, we find that the typical network characteristics, while very revealing, do not tell the whole story. In particular, the Italian mobility network during lockdown has been damaged much more than node- and edge-level metrics indicate. Additionally, many of the main Provinces of Italy are affected by the lockdown in a surprisingly similar fashion, despite their geographical and economic dissimilarity. Based on our findings we offer an approach to estimate unavailable high-resolution economic dimensions, such as real time Province-level GDP, based on easily measurable mobility information.

Assessing the cascading impacts of natural disasters in a multi-layer behavioral network framework

Natural disasters negatively impact regions and exacerbate socioeconomic vulnerabilities. While the direct impacts of natural disasters are well understood, the channels through which these shocks spread to non-affected regions, still represents an open research question. In this paper we propose modelling socioeconomic systems as spatially-explicit, multi-layer behavioral networks, where the interplay of supply-side production, and demand-side consumption decisions, can help us understand how climate shocks cascade. We apply this modelling framework to analyze the spatial-temporal evolution of vulnerability following a negative food-production shock in one part of an agriculture-dependent economy. Simulation results show that vulnerability is cyclical, and its distribution critically depends on the network density and distance from the epicenter of the shock. We also introduce a new multi-layer measure, the Vulnerability Rank (VRank), which synthesizes various location-level risks into a single index. This framework can help design policies, aimed to better understand, effectively respond, and build resilience to natural disasters. This is particularly important for poorer regions, where response time is critical and financial resources are limited.

Percolation of attack with tunable limited knowledge

Percolation models shed a light on network integrity and functionality and have numerous applications in network theory. This paper studies a targeted percolation (α model) with incomplete knowledge where the highest degree node in a randomly selected set of n nodes is removed at each step, and the model features a tunable probability that the removed node is instead a random one. A "mirror image" process (β model) in which the target is the lowest degree node is also investigated. We analytically calculate the giant component size, the critical occupation probability, and the scaling law for the percolation threshold with respect to the knowledge level n under both models. We also derive self-consistency equations to analyze the k-core organization including the size of the k core and its corona in the context of attacks under tunable limited knowledge. These percolation models are characterized by some interesting critical phenomena and reveal profound quantitative structure discrepancies between Erdős-Rényi networks and power-law networks.

Systemic stress test model for shared portfolio networks

We propose a dynamic model for systemic risk using a bipartite network of banks and assets in which the weight of links and node attributes vary over time. Using market data and bank asset holdings, we are able to estimate a single parameter as an indicator of the stability of the financial system. We apply the model to the European sovereign debt crisis and observe that the results closely match real-world events (e.g., the high risk of Greek sovereign bonds and the distress of Greek banks). Our model could become complementary to existing stress tests, incorporating the contribution of interconnectivity of the banks to systemic risk in time-dependent networks. Additionally, we propose an institutional systemic importance ranking, BankRank, for the financial institutions analyzed in this study to assess the contribution of individual banks to the overall systemic risk.