Characterization of robustness and resilience in graphs: a mini-review

We briefly survey recent proposals that seek to capture in numerical terms the resilience and the robustness of a graph. After a brief introduction and the establishment of notation and terminology, we catalogue characterizations proposed in journal articles published within the last two decades. We then describe some of the numerous application areas for such characterizations. We experiment with implementations of numerous characteristics on several graph-generation models, after which we conclude with a discussion of open problems and future directions.

Automated summary

In this paper, recent proposals aiming to quantify the resilience and robustness of a graph in numerical terms are briefly surveyed, with characterizations from journal articles published in the last two decades catalogued. The various applications of these characterizations are then described. Through experimentation with implementations on several graph-generation models, open problems and future directions are analyzed in the conclusion.