The response of a network to connectivity disruption is central to understanding its robustness. While such questions have been thoroughly studied in terms of global cohesion, many questions remain open regarding the impact on local connectivity. Specifically, networks with different topologies display different distributions of small motifs, and it remains unclear how local connectivity patterns link to structural weaknesses within a network. This study presents a principled approach for assessing random connectivity disruptions among the nodes of a network to identify its structural vulnerabilities. Leveraging recent findings on random walks for exact local topology recollection, we introduce a method for quantifying changes within the (l)-hop neighborhood of the nodes. We derive vulnerability profiles for the nodes and introduce a new index that aggregates neighboring nodes’ vulnerabilities in a distance dependent weighting. Our conducted experiments show that structural weaknesses of a network are distributed across localized regions, where vulnerabilities are most likely driven by immediate neighborhoods of the nodes.
Zakroum et al. (Sun,) studied this question.