Developing accurate metrics to evaluate the resilience of large-scale networks, e.g., critical infrastructures, plays a pivotal role in secure operation of these networks. In this paper, we propose a novel framework to study the resilience of a network. To this end, we leverage the tools from Topological Data Analysis (TDA) and Persistent Homology (PH). The combined deployment of TDA and PH tools provides us with a solid understanding of network topology only based on the underlying weighted graph and comparing it with the base network, e.g., fully connected network as the most resilient structure. By utilizing an abstract network to build our arguments and results, we present a step-by-step method to leverage the fundamental theories of TDA to study and improve a network’s resilience. By creating a weighted graph, where weights represent a meaningful attribute to the underlying network, we utilize Vietori–Rips complex and filtration to create persistent diagrams. This allows us to extract topological information to study network resilience. Further, we show how the use of Wasserstein distances can provide detailed information about the critical edges (e.g., roads in transportation networks, or power distribution lines in power networks) in the network, and how adding or removing certain edges affect the level of resilience of the network by presenting a novel metric to quantify the resilience of a network. We evaluate the effectiveness of the proposed method using a case study that compares a base network with networks that include different edges using our resilience metric.