Abstract
Critical services depend on infrastructure networks for their operation and any disruption to these networks can have significant impacts on society, the economy, and quality of life. Such networks can be characterised as graphs which can be used to understand their structural properties, and the effect on their behaviour and robustness to hazards. Using a suite of graphs and critical infrastructure networks, this study aims to show that networks which exhibit a hierarchical structure are more likely to be less robust comparatively to non-hierarchical networks when exposed to failures, including those which supply critical services. This study investigates the properties of a hierarchical structure through identifying a set of key characteristics from an ensemble of graph models which are then used in a comparative analysis against a suite of spatial critical infrastructure networks. A failure model is implemented and applied to understand the implications of hierarchical structures in real world networks for their robustness to perturbations. The study concludes that a set of three graph metrics, cycle basis, maximum betweenness centrality and assortativity coefficient, can be used to identify the extent of a hierarchy in graphs, where a lack of robustness is linked to the hierarchical structure, a feature exhibited in both graph models and infrastructure networks.
Highlights
Infrastructure networks are critical to the functioning of modern societies, with a significant and growing dependence on them for everyday activities and quality of life (Boin and McConnell 2007; Cabinet Office 2010; Sterbenz et al 2011)
The results have clearly indicated that hierarchical networks are distinctive from nonhierarchical networks, both with regard to the structural characteristics as observed through the assortativity coefficient, maximum betweenness centrality and the number of cycle basis, as well through the response to perturbations
The characteristics of hierarchically organised networks have been explored, identifying the key measures which can be used to begin to distinguish between hierarchical and non-hierarchical networks. This has led to the recognition that many real world spatial critical infrastructure networks are hierarchically-structured, and as a result exhibit a weak robustness to perturbations, especially those which affect critical nodes within the network
Summary
Infrastructure networks are critical to the functioning of modern societies, with a significant and growing dependence on them for everyday activities and quality of life (Boin and McConnell 2007; Cabinet Office 2010; Sterbenz et al 2011). They are often found to be vulnerable to failures, with numerous incidents reported which have led to widespread disruption at large economic costs (Rinaldi et al 2001; Andersson et al 2005; Royal Academy of Engineering 2014; OFCOM 2018; OFWAT 2018; National Infrastructure Commission 2020; OFGEM 2020). This can result in a different set of characterisation methods being required, with the potential for new network organisational features to be identified
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