Percolation Thresholds for Robust Network Connectivity

TL;DR

This paper investigates new percolation thresholds that ensure not only network connectivity but also robustness against failures, providing insights into the resilience of various network structures.

Contribution

It introduces and analyzes four measures of robust connectivity and evaluates their thresholds on 2D lattice networks, advancing understanding of network resilience.

Findings

Identified four measures of robust connectivity.

Numerically evaluated robust percolation thresholds.

Provided insights into network resilience and robustness.

Abstract

Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to mobility, node or edge failures, and varying traffic loads. Percolation theory quantifies the threshold value of a local control parameter such as a node occupation (resp., deletion) probability or an edge activation (resp., removal) probability above (resp., below) which there exists a giant connected component (GCC), a connected component comprising of a number of occupied nodes and active edges whose size is proportional to the size of the network itself. Any pair of occupied nodes in the GCC is connected via at least one path comprised of active edges and occupied nodes. The mere existence of the GCC itself does not guarantee that the long-range connectivity would be robust, e.g., to random link or node failures due to network dynamics. In this paper, we explore new percolation thresholds that guarantee not only spanning network connectivity, but also robustness. We define and analyze four measures of robust network connectivity, explore their interrelationships, and numerically evaluate the respective robust percolation thresholds for the 2D square lattice.