Resilience or robustness: identifying topological vulnerabilities in rail networks

Assessing the dynamic resilience of Urban Rail Transit Networks during their evolution using a ridership-weighted network

The assessment of the resilience of Urban Rail Transit Networks (URTNs) and the analysis of their evolutionary characteristics during network growth can help in the design of efficient, safe, and sustainable networks. However, there have been few studies regarding the change of resilience in long-term network development. As for the existing resilience studies, they rarely consider the entire cycle of accident occurrence and repair; furthermore, they ignore the changes in network transportation performance during emergencies. Moreover, the measurement metrics of the important nodes have not been comprehensively considered. Therefore, to remedy these deficiencies, this paper proposes a URTN dynamic resilience assessment model that integrates the entire cycle of incident occurrence and repair, and introduces the network transport effectiveness index E(Gw) to quantitatively assess the network resilience. In addition, a weighted comprehensive identification method of the important nodes (the WH method) is proposed. The application considers the Xi'an urban rail transit network (XURTN) during 2011-2021. The obtained results identify the resilience evolutionary characteristics during network growth. And longer peripheral lines negatively affect the resilience of XURTN during both the attack and the repair processes. The central city network improves the damage index Rdam and the recovery index Rrec by up to 123.46% and 11.65%, respectively, over the overall network. In addition, the WH method can comprehensively and accurately identify the important nodes in the network and their evolutionary characteristics. Compared to the single-factor and topological strategies, the Rdam is 1.17%~178.89% smaller and the Rrec is 1.68%~84.81% larger under the WH strategy. Therefore, this method improves the accuracy of the important node identification. Overall, the insights from this study can provide practical and scientific references for the synergistic development of URTN and urban space, the enhancement of network resilience, and the protection and restoration of important nodes.

Influence and influenceability: global directionality in directed complex networks

Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of trophic analysis to study directed networks and show that both 'influence' and 'influenceability' in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localizes; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalized rock-paper-scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted-that node hierarchy is essential for understanding network influence, mediated by global directionality-are applicable to many real-world dynamics.

Strong connectivity in real directed networks

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behavior of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering-a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes and confirm our results on many real-world networks, including ecological, neural, trade, and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. This means that many dynamical processes on networks can depend significantly on a small fraction of edges.

Uncertainty quantification of multi-scale resilience in networked systems with nonlinear dynamics using arbitrary polynomial chaos

Complex systems derive sophisticated behavioral dynamics by connecting individual component dynamics via a complex network. The resilience of complex systems is a critical ability to regain desirable behavior after perturbations. In the past years, our understanding of large-scale networked resilience is largely confined to proprietary agent-based simulations or topological analysis of graphs. However, we know the dynamics and topology both matter and the impact of model uncertainty of the system remains unsolved, especially on individual nodes. In order to quantify the effect of uncertainty on resilience across the network resolutions (from macro-scale network statistics to individual node dynamics), we employ an arbitrary polynomial chaos (aPC) expansion method to identify the probability of a node in losing its resilience and how the different model parameters contribute to this risk on a single node. We test this using both a generic networked bi-stable system and also established ecological and work force commuter network dynamics to demonstrate applicability. This framework will aid practitioners to both understand macro-scale behavior and make micro-scale interventions.

Research on the Destruction Resistance of Giant Urban Rail Transit Network from the Perspective of Vulnerability

Giant urban rail transit (GURT) systems have been formed in many metropolises and play a critical role in addressing serious traffic congestion. Unfortunately, as a dynamic and complex system, the vulnerability of GURT networks under various failure scenarios will be more prominent as the network expansion continues. Thus, it is imperative to explore the complex structural characteristics of the network and improve the ability to deal with the disturbance of emergencies. In this study, the destruction resistance of GURT networks with scale growth is illustrated from a vulnerability perspective. Specifically, taking Shanghai rail transit (SHRT) system as an example, the network topology model is constructed using the Space L method, and the network structure characteristics are analyzed based on the complex network theory. In addition, five attack strategies are developed to represent random and targeted attacks during the simulation of network failure, and two metrics are determined to evaluate the network vulnerability. Some meaningful results have been obtained: (i) The Shanghai rail transit planning network (SHRTPN) has increased the network efficiency by more than 10% over the Shanghai rail transit operating network (SHRTON) and has effectively enhanced the network destruction resistance. (ii) The SHRT network is a small-world network and shows significant vulnerability under the targeted attacks. The failure of only 3% high betweenness stations in SHRTON can lead to a 66.2% decrease in the network efficiency and a 75.8% decrease in the largest connected component (LCC) ratio. (iii) Attacking stations will cause more severe network failures than attacking edges, and it is necessary to focus on preventing catastrophic network failure caused by the critical station’s failure breaking the threshold. Finally, the strategies for improving the destruction resistance of GURT networks are proposed. The findings of this research can provide an essential reference for the rational planning, safety protection, and sustainable construction of GURT systems.

Network hierarchy and pattern recovery in directed sparse Hopfield networks

Many real-world networks are directed, sparse, and hierarchical, with a mixture of feedforward and feedback connections with respect to the hierarchy. Moreover, a small number of master nodes are often able to drive the whole system. We study the dynamics of pattern presentation and recovery on sparse, directed, Hopfield-like neural networks using trophic analysis to characterize their hierarchical structure. This is a recent method which quantifies the local position of each node in a hierarchy (trophic level) as well as the global directionality of the network (trophic coherence). We show that even in a recurrent network, the state of the system can be controlled by a small subset of neurons which can be identified by their low trophic levels. We also find that performance at the pattern recovery task can be significantly improved by tuning the trophic coherence and other topological properties of the network. This may explain the relatively sparse and coherent structures observed in the animal brain and provide insights for improving the architectures of artificial neural networks. Moreover, we expect that the principles we demonstrate here, through numerical analysis, will be relevant for a broad class of system whose underlying network structure is directed and sparse, such as biological, social, or financial networks.

Geographic delay characterization of railway systems

Railway systems provide pivotal support to modern societies, making their efficiency and robustness important to ensure. However, these systems are susceptible to disruptions and delays, leading to accumulating economic damage. The large spatial scale of delay spreading typically make it difficult to distinguish which regions will ultimately affected from an initial disruption, creating uncertainty for risk assessment. In this paper, we identify geographical structures that reflect how delay spreads through railway networks. We do so by proposing a graph-based, hybrid schedule and empirical-based model for delay propagation and apply spectral clustering. We apply the model to four European railway systems: the Netherlands, Germany, Switzerland and Italy. We characterize these geographical delay structures in the railway systems of these countries and interpret these regions in terms of delay severity and how dynamically disconnected they are from the rest. The method also allows us to point out important differences between these countries' railway systems. For practitioners, such geographical characterization of railways provides natural boundaries for local decision-making structures and risk assessment.

Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks

Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their functional properties, partition and rank the vertices accordingly. Trophic levels and hence trophic coherence can only be defined on graphs with basal vertices, i.e. vertices with zero in-degree. Consequently, trophic analysis of graphs had been restricted until now. In this paper we introduce a hierarchical framework which can be defined on any simple graph. Within this general framework, we develop several metrics: hierarchical levels, a generalisation of the notion of trophic levels, influence centrality, a measure of a vertex's ability to influence dynamics, and democracy coefficient, a measure of overall feedback in the system. We discuss how our generalisation relates to previous attempts and what new insights are illuminated on the topological and dynamical aspects of graphs. Finally, we show how the hierarchical structure of a network relates to the incidence rate in a SIS epidemic model and the economic insights we can gain through it.

Dynamic Complex Network Analysis of PM2.5 Concentrations in the UK, Using Hierarchical Directed Graphs (V1.0.0)

The risk of a broad range of respiratory and heart diseases can be increased by widespread exposure to fine atmospheric particles on account of their capability to have a deep penetration into the blood streams and lung. Globally, studies conducted epidemiologically in Europe and elsewhere provided the evidence base indicating the major role of PM2.5 leading to more than four million deaths annually. Conventional approaches to simulate atmospheric transportation of particles having high dimensionality from both transport and chemical reaction process make exhaustive causal inference difficult. Alternative model reduction methods were adopted, specifically a data-driven directed graph representation, to deduce causal directionality and spatial embeddedness. An undirected correlation and a directed Granger causality network were established through utilizing PM2.5 concentrations in 14 United Kingdom cities for one year. To demonstrate both reduced-order cases, the United Kingdom was split up into two southern and northern connected city communities, with notable spatial embedding in summer and spring. It continued to reach stability to disturbances through the network trophic coherence parameter and by which winter was construed as the most considerable vulnerability. Thanks to our novel graph reduced modeling, we could represent high-dimensional knowledge in a causal inference and stability framework.

Cascading dominates large-scale disruptions in transport over complex networks

The core functionality of many socio-technical systems, such as supply chains, (inter)national trade and human mobility, concern transport over large geographically-spread complex networks. The dynamical intertwining of many heterogeneous operational elements, agents and locations are oft-cited generic factors to make these systems prone to large-scale disruptions: initially localised perturbations amplify and spread over the network, leading to a complete standstill of transport. Our level of understanding of such phenomena, let alone the ability to anticipate or predict their evolution in time, remains rudimentary. We approach the problem with a prime example: railways. Analysing spreading of train delays on the network by building a physical model, supported by data, reveals that the emergence of large-scale disruptions rests on the dynamic interdependencies among multiple 'layers' of operational elements (resources and services). The interdependencies provide pathways for the so-called delay cascading mechanism, which gets activated when, constrained by local unavailability of on-time resources, already-delayed ones are used to operate new services. Cascading locally amplifies delays, which in turn get transported over the network to give rise to new constraints elsewhere. This mechanism is a rich addition to some well-understood ones in, e.g., epidemiological spreading, or the spreading of rumours and opinions over (contact) networks, and stimulates rethinking spreading dynamics on complex networks. Having these concepts built into the model provides it with the ability to predict the evolution of large-scale disruptions in the railways up to 30-60 minutes up front. For transport systems, our work suggests that possible alleviation of constraints as well as a modular operational approach would arrest cascading, and therefore be effective measures against large-scale disruptions.

Answerable and Unanswerable Questions in Risk Analysis with Open-World Novelty

Decision analysis and risk analysis have grown up around a set of organizing questions: what might go wrong, how likely is it to do so, how bad might the consequences be, what should be done to maximize expected utility and minimize expected loss or regret, and how large are the remaining risks? In probabilistic causal models capable of representing unpredictable and novel events, probabilities for what will happen, and even what is possible, cannot necessarily be determined in advance. Standard decision and risk analysis questions become inherently unanswerable ("undecidable") for realistically complex causal systems with "open-world" uncertainties about what exists, what can happen, what other agents know, and how they will act. Recent artificial intelligence (AI) techniques enable agents (e.g., robots, drone swarms, and automatic controllers) to learn, plan, and act effectively despite open-world uncertainties in a host of practical applications, from robotics and autonomous vehicles to industrial engineering, transportation and logistics automation, and industrial process control. This article offers an AI/machine learning perspective on recent ideas for making decision and risk analysis (even) more useful. It reviews undecidability results and recent principles and methods for enabling intelligent agents to learn what works and how to complete useful tasks, adjust plans as needed, and achieve multiple goals safely and reasonably efficiently when possible, despite open-world uncertainties and unpredictable events. In the near future, these principles could contribute to the formulation and effective implementation of more effective plans and policies in business, regulation, and public policy, as well as in engineering, disaster management, and military and civil defense operations. They can extend traditional decision and risk analysis to deal more successfully with open-world novelty and unpredictable events in large-scale real-world planning, policymaking, and risk management.

Organisational Social Influence on Directed Hierarchical Graphs, from Tyranny to Anarchy

Coordinated human behaviour takes place within a diverse range of social organisational structures, which can be thought of as power structures with "managers" who influence "subordinates". A change in policy in one part of the organisation can cause cascades throughout the structure, which may or may not be desirable. As organisations change in size, complexity and structure, the system dynamics also change. Here, we consider majority rule dynamics on organisations modelled as hierarchical directed graphs, where the directed edges indicate influence. We utilise a topological measure called the trophic incoherence parameter, q, which effectively gauges the stratification of power structure in an organisation. We show that this measure bounds regimes of behaviour. There is fast consensus at low q (e.g. tyranny), slow consensus at mid q (e.g. democracy), and no consensus at high q (e.g. anarchy). These regimes are investigated analytically, numerically and empirically with diverse case studies in the Roman Army, US Government, and a healthcare organisation. Our work demonstrates the usefulness of the trophic incoherence parameter when considering models of social influence dynamics, with widespread consequences in the design and analysis of organisations.

Network robustness improvement via long-range links

Many systems are today modelled as complex networks, since this representation has been proven being an effective approach for understanding and controlling many real-world phenomena. A significant area of interest and research is that of networks robustness, which aims to explore to what extent a network keeps working when failures occur in its structure and how disruptions can be avoided. In this paper, we introduce the idea of exploiting long-range links to improve the robustness of Scale-Free (SF) networks. Several experiments are carried out by attacking the networks before and after the addition of links between the farthest nodes, and the results show that this approach effectively improves the SF network correct functionalities better than other commonly used strategies.