Resilience or robustness: identifying topological vulnerabilities in rail networks

Pagani, Alessio; Mosquera, Guillem; Alturki, Aseel; Johnson, Samuel; Jarvis, Stephen A.; Wilson, Alan; Guo, Weisi; Varga, Liz

doi:10.1098/rsos.181301

Cited by 54 publications

(41 citation statements)

References 41 publications

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“…9 Route classification: a, b Cumulative distribution of route distance for different years. c Number of routes for different distance classes either explicitly through differential equation models [42] or using passenger flow data as a proxy [43]. Fig.…”

Section: Discussionmentioning

confidence: 99%

Global air transport complex network: multi-scale analysis

et al. 2019

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Almost half of the world's population is carried by airlines each year, and understanding this mode of transport is important from economic and scientific perspectives. In recent years, the increasing availability of data has led to complex network and agent interaction models which attempt to gain better understanding of the air transport network and develop forecasts. In this case study paper, we review existing research on two key approaches, namely: (1) a top-down multi-scale network science approach, and (2) a bottom-up entropy-maximization interaction network approach. Using simple socioeconomic indicators, we were able to construct a very accurate interaction model that can predict traffic volume, and the model can forward estimate the impact of population growth or fuel cost. Using network science approaches, we were able to identify community structures and relate them to economic outputs. We also saw how hubs evolved over time to become more influential. Looking into the future, using random graph theory, it seems that reduced flight cost will lead to increased hub influence. The disseminated knowledge in this case study paper will provide both academics and industry practitioners with steps forward to co-explore the interesting research landscape.• Bottom-up entropy-maximization interaction model, which considers consumer choice; • Top-down network science analysis, which seeks to uncover common statistical patterns and infer latent knowledge.The former gives a complex and detailed understanding of how spatial networks (i.e., flights) form from spatial processes (i.e., airports) and what the weight of each edge (i.e., passenger volume) is with respect to cost (impedes flow) and benefit (attracts flow) functions that relate to consumer behaviour. The latter approach gives a statistical understanding into the fundamental network properties and how they evolve over time, enabling the application of generalized network scaling laws that can be used to predict the future structure of the network. Both the bottomup and the top-down approach is of fundamental interest to network science and industry.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Section: Discussionmentioning

confidence: 99%

Global air transport complex network: multi-scale analysis

et al. 2019

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“…Some species do not fit neatly into an integer trophic level, for example a scavenger like a rat may feed on plants as well as the dead bodies of sheep and wolves 11 . The concept of describing directed networks with energy flow has been extended beyond food webs, for instance to inferring multi-scale stability in both transportation networks 16 and water distribution systems 28 .…”

Section: Methodsmentioning

confidence: 99%

“…Trophic coherence has been called a measure of how similar a graph is to a hierarchy 16 , with a hierarchy being maximally coherent with trophic incoherence parameter, q = 0 ( Fig. 1(c)).…”

Section: Methodsmentioning

confidence: 99%

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

Pilgrim

Guo

Johnson

2020

Sci Rep

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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.Social and political systems display different types of order and structure, with very different outcomes. Small-scale informal organisations might be skill or power based, whereas large-scale social systems often involve complex politics. Some form of formal or latent hierarchy is present in almost all social organisations. Traditional military organisations are perhaps the prototypical example of rigid hierarchy, with a very ordered structure allowing instructions to be quickly passed from top to bottom 1 . While these kinds of singular hierarchies abound historically 2 , in the 18th Century the influential treatise "The Spirit of the Laws" laid down a political theory that rejected hierarchical structure of government and called for a separation of powers 3 , i.e. balancing power between multiple hierarchies. Influenced by this treatise and other enlightenment thinking, the US Constitution, which among other things dictates the structure of the US Government, prescribes a series of checks and balances with the explicit intention of preventing a singular tyrannical exploitation of power 4 . On the other end of the scale, political anarchy has been described as a rejection of any form of hierarchy 5 . Anarchy should not be dismissed as disorganised chaos -there are movements in management 2 and organisational 6 science that encourage self-empowered individuals working autonomously or in dynamically forming teams, with an organisational structure resembling that of political anarchy. One can regard anarchy as a non-equilibrium form of hierarchy, whereby at any particular quasi-static state, a power hierarchy exists. In between these extremes, modern democracies (on average) can be considered more distributed than rigid tyrannical hierarchies and more ordered than p...

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“…where aij is the adjacency matrix of the graph and is the number of in-neighbours of the node i. Basal nodes have trophic level by convention (Pagani et al, 2019). In our study, to define trophic coherence in a directed causal network, the first step was defining basal nodes.…”

Section: Trophic Coherencementioning

confidence: 99%

Dynamic Complex Network Analysis of PM<sub>2.5</sub> Concentrations in the UK using Hierarchical Directed Graphs (V1.0.0)

Broomandi¹,

Geng²,

Guo³

et al. 2020

Preprint

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Worldwide exposure to fine atmospheric particles can exasperate the risk of a wide range of heart and respiratory diseases, due to their ability to penetrate deep into the lungs and blood streams. Epidemiological studies in Europe and elsewhere have established the evidence base pointing to the important role of PM2.5 (fine particles with a diameter of 2.5 microns or less) in causing over 4 million deaths per year. Traditional approaches to model atmospheric transportation of particles suffer from high dimensionality from both transport and chemical reaction processes, making multi-sale causal inference challenging. We apply alternative model reduction methods -a data-driven directed graph representation to infer spatial embeddedness and causal directionality. Using PM2.5 concentrations in 14 UK cities over a 12month period, we construct an undirected correlation and a directed Granger causality network.We show for both reduced-order cases, the UK is divided into two a northern and southern connected city communities, with greater spatial embedding in spring and summer. We go on to infer stability to disturbances via the network trophic coherence parameter, whereby we found that winter had the greatest vulnerability. As a result of our novel graph-based reduced modeling, we are able to represent high-dimensional knowledge into a causal inference and stability framework.

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Resilience or robustness: identifying topological vulnerabilities in rail networks

Cited by 54 publications

References 41 publications

Global air transport complex network: multi-scale analysis

Global air transport complex network: multi-scale analysis

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

Dynamic Complex Network Analysis of PM<sub>2.5</sub> Concentrations in the UK using Hierarchical Directed Graphs (V1.0.0)

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Resilience or robustness: identifying topological vulnerabilities in rail networks

Cited by 54 publications

References 41 publications

Global air transport complex network: multi-scale analysis

Global air transport complex network: multi-scale analysis

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

Dynamic Complex Network Analysis of PM&lt;sub&gt;2.5&lt;/sub&gt; Concentrations in the UK using Hierarchical Directed Graphs (V1.0.0)

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Product

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Dynamic Complex Network Analysis of PM<sub>2.5</sub> Concentrations in the UK using Hierarchical Directed Graphs (V1.0.0)