Vulnerability of Transport through Evolving Spatial Networks

TL;DR

This paper investigates the vulnerability of evolving spatial networks to blockages, revealing self-similar patterns and fractal properties that help predict when networks become impenetrable, with implications for infrastructure resilience.

Contribution

It introduces a recursive method to identify critical hubs in porous networks and characterizes the fractal nature of the blockage backbone, advancing understanding of network failure mechanisms.

Findings

Blockage backbone is a self-similar path with a fractal dimension.

Number of blocking steps collapses onto a master curve across network sizes.

Shortest-path length distribution broadens during blocking, indicating increased spatial correlations.

Abstract

Insight into the blockage vulnerability of evolving spatial networks is important for understanding transport resilience, robustness, and failure of a broad class of real-world structures such as porous media and utility, urban traffic, and infrastructure networks. By exhaustive search for central transport hubs on porous lattice structures, we recursively determine and block the emerging main hub until the evolving network reaches the impenetrability limit. We find that the blockage backbone is a self-similar path with a fractal dimension which is distinctly smaller than that of the universality class of optimal path crack models. The number of blocking steps versus the rescaled initial occupation fraction collapses onto a master curve for different network sizes, allowing for the prediction of the onset of impenetrability. The shortest-path length distribution broadens during the blocking process reflecting an increase of spatial correlations. We address the reliability of our predictions upon increasing the disorder or decreasing the fraction of processed structural information.