A Graph Resilience Metric Based On Paths: Higher Order Analytics With GPU

Structural resilience is an inherent, paramount property of real world, massive, scale free graphs such as those typically encountered in brain networks, protein-to-protein interaction diagrams, logistics and supply chains, as well as social media among others. This means that in case a small fraction of edges or even vertices with their incident edges are deleted, then alternative, although possibly longer, paths can be found such that the overall graph connectivity remains intact. This durability, which is constantly exhibited in nature, can be attributed to three main reasons. First, almost by construction, scale free graphs have a relatively high density. Moreover, they have a short diameter or at least an effective diameter. Finally, scale free graphs are recursively built on communities. As a consequence, the effect of a few edge or even vertex deletions inside a community remains isolated there as a rule and the effects of deletion are thus negated. Ultimately these properties stem from the degree distribution. In this conference paper is proposed a new, generic, and scalable graph resilience metric which relies on the weighted sum of the number of paths crossing certain vertices of great communication and structural value. Finally, the CUDA implementation is discussed and compared to a serial one in mex. The metric performance is assessed in terms of total computational time and parallelism.