On the Impact of the Embedding Process on Network Resilience Quantification

Network resilience is crucial to ensure reliable and secure operation of critical infrastructures. Although graph theoretic methods have been developed to quantify the topological resilience of networks, i.e., measuring resilience with respect to connectivity, in this study we propose to use the tools from Topological Data Analysis (TDA), Algebraic Topology, and Optimal Transport (OT). In our prior work, we used these tools to create a resilience metric that bypassed the need to embed a network onto a space. We also hypothesized that embeddings could encode different information about a network and that different embeddings could result in different outcomes when computing resilience. In this paper we attempt to test this hypothesis. We will utilize the WEGL framework to compute the embedding for the considered network and compare the results against our prior work, which did not use an embedding process. To our knowledge, this is the first attempt to study the ramifications of choosing an embedding, thus providing a novel understanding into how to choose an embedding and whether such a choice matters when quantifying resilience.