The extreme vulnerability of interdependent spatially embedded networks

TL;DR

This paper reveals that interdependent spatially embedded networks, such as power grids, are extremely vulnerable to failures, with even minimal interdependence causing abrupt systemic collapse, unlike non-embedded networks.

Contribution

The study analytically and numerically demonstrates that interdependent lattice networks lack a critical dependency threshold, making them highly susceptible to cascading failures from minimal interdependence.

Findings

Any small fraction of interdependent nodes causes abrupt collapse in lattice networks.

Lattice networks exhibit no critical dependency threshold, unlike random networks.

The vulnerability is linked to the percolation transition properties of the lattice.

Abstract

Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this "critical dependency" (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and \textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.