Comparing spatial networks: A one-size-fits-all efficiency-driven approach

Abstract

Spatial networks are a very powerful framework for studying a large variety of systems which can be found in a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few. Spatial networks can be defined by their total cost (generally understood as the total amount of resources needed for building or traveling their connections). Here, we address the issue of how to gauge and compare the quality of spatial network designs (i.e. efficiency vs. total cost) by proposing a two-step methodology. Firstly, we introduce a quality function to assess the overall performance of any network. Second, we propose an algorithm to estimate computationally the upper bound of our quality function for a given specific network. The smaller is the difference between such an upper bound and the empirical value, the higher we consider the design quality of the network under analysis to be. In order to avoid scalability limitations when applying this second step on large networks, we provide a universal expression to obtain an approximated upper bound to any network. Finally, we test the applicability of this analytic tool-set on spatial network datasets of different nature.

Ensembles of realistic power distribution networks

“…Among these works, Riba et al ( 45 ) have used Hausdorff distance between nodes in the network to compare network geometries. Morer et al ( 46 ) include edge geometry–based comparison and propose an “efficiency” metric to measure the distance of a network (where edges have nonstraight-line geometries between nodes) from its most optimal version (where each edge has a straight-line geometry).…”

Efficiency and shrinking in evolving networks

“…The evolution of networks has been the subject of numerous studies and books [1][2][3][4] and concerns different fields, ranging from biology to transportation engineering [5][6][7]. Many measures were defined and many models were proposed to describe the growth of these systems, but some important questions remain unanswered.…”

“…While these are interesting examples, these networks probably evolve through very different processes compared to man-made infrastructures, such as roads, railways or pipelines, where planning is often centralized. For transport infrastructures, the main design goal is to obtain a high transport capacity at a reasonable cost: cost and efficiency appear naturally as critical parameters governing the formation and evolution of these systems, sometimes at the expense of resilience [3,4,6,7]. In the case of railway systems, in addition to the coupling with the population density, the network is also affected by technological advances that propose new and faster means which can be a cause of shrinking effects in these networks: older, slower lines can be abandoned as new faster lines appear, resulting in a global decrease in the total length of the network and its number of nodes.…”