Author:
Sperry Megan M.,Telesford Qawi K.,Klimm Florian,Bassett Danielle S.
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.
Funder
National Institute of Health
Engineering and Physical Sciences Research Council’ and ’Medical Research Council
Army Research Laboratory
Army Research Office
National Institute of Mental Health
National Institute of Child Health and Human Development
Office of Naval Research
National Science Foundation
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,Control and Optimization,Management Science and Operations Research,Computer Networks and Communications
Reference49 articles.
1. Efficient behavior of small-world
networks.;Latora,;Phys. Rev. Lett.,2001
2. Spatial
networks.;Barthlemy,;Phys. Rep.,2011
3. Paradigms of connectivity for computer
circuits and networks.;Ozaktas,;Opt. Eng.,1992
4. Nonoptimal component placement, but short processing paths, due to
long-distance projections in neural systems.;Kaiser,;PLoS Computational
Biology,2006
5. Efficient physical embedding of topologically complex information
processing networks in brains and computer circuits.;Bassett,;PLoS Comput.
Biol.,2010
Cited by
17 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献