Rentian scaling for the measurement of optimal embedding of complex networks into physical space
Year: 2016
Type: article
Abstract: The London Underground is one of the largest, oldest and most widely used systems of public transit in the world. Transportation in London is constantly challenged to expand and adapt its system to meet the changing requirements of London's populace while maintaining a cost-effective and efficient network. Previous studies have described this system using concepts from graph theory, reporting network diagnostics and core-periphery architecture. These studies provide information about the basic structure and efficiency of this network; however, the question of system optimization in the context of evolving demands is seldom investigated. In this paper we examined the cost effectiveness of the topological-physical embedding of the Tube using estimations of the topological dimension, wiring length and Rentian scaling, an isometric scaling relationship between the number of elements and connections in a system. We measured these properties in both two- and three-dimensional embeddings of the networks into Euclidean space, as well as between two time points, and across the densely interconnected core and sparsely interconnected periphery. While the two- and three-dimensional representations of the present-day Tube exhibit Rentian scaling relationships between nodes and edges of the system, the overall network is approximately cost-efficiently embedded into its physical environment in two dimensions, but not in three. We further investigated a notable disparity in the topology of the network's local core versus its more extended periphery, suggesting an underlying relationship between meso-scale structure and physical embedding. The collective findings from this study, including changes in Rentian scaling over time, provide evidence for differential embedding efficiency in planned versus self-organized networks. These findings suggest that concepts of optimal physical embedding can be applied more broadly to other physical systems whose links are embedded in a well-defined space, and whose topology is constrained by a cost function that minimizes link lengths within that space.
Source: Journal of Complex Networks
Institutions: University of Oxford, University of Pennsylvania
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: University of Bristol, National Institutes of Health, Engineering and Physical Sciences Research Council, National Science Foundation of Sri Lanka, Office of Naval Research, National Institute of Mental Health, National Institute on Deafness and Other Communication Disorders, National Institute of Arthritis and Musculoskeletal and Skin Diseases, National Institute of Child Health and Human Development, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Army Research Office, Army Research Laboratory
Awards: G1099660080, G1997747098, G2252567680, G235261508, G2425642435, G3137615481, G3824545241, G572628577, G6738641543, Linguistic and Nonlinguistic Functions of Frontal Cortex, CRCNS: US-France Modeling & Predicting BCI Learning from Dynamic Networks, Training Program in Musculoskeletal Research, G987310051
OpenAlex ID: W2497767833