k-connectivity for confined random networks

TL;DR

This paper derives formulas for the probability that a confined random network remains fully connected after node removals, highlighting the influence of domain shape on network robustness.

Contribution

It provides the first closed-form analytic expressions for k-connectivity probabilities in confined random networks, emphasizing the role of domain geometry.

Findings

k-connectivity depends on domain shape, especially corners

Formulas enable better network design for robustness

Results applicable to wireless and sensor networks

Abstract

k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability that a confined random network remains fully connected after the removal of k-1 nodes. Our analysis reveals that k-connectivity is governed by microscopic details of the network domain such as sharp corners rather than the macroscopic total volume. Hence, our results can aid in the design of reliable networks, an important problem in e.g. wireless ad hoc and sensor networks.