The objective of civil infrastructure design is to provide the best service possible within execution constraints, for a given lifetime service. During this lifetime exceptional events occur which stress the working limits beyond regular performance and may even collapse functionality completely. Modern frameworks to assess quantitatively these situations are based on the concept of resilience; broadly describing system behavior during, in the immediate aftermath, and recovery phases of the infrastructure. We are usually interested in a level of service provided by these networks in the form of flow ease, quality, and capacity. Network infrastructures are complex systems that can be readily represented as graph objects. Traditional literature classifies different approaches as topological, flow-based, or statistical as they try to recognize different aspects of the network structure that reflect their resilience and reliability. Although most reliability analysis for networks uses concepts from graph theory to assess reliability, these metrics fall short when informing investment decisions on practical quantities. Alternatively, flow metrics are used but require assumptions on the flow mechanics and become difficult to analyze probabilistically in reasonable computational time. This work aims to condense all these aspects relevant to network infrastructure resilience in a single approach, produce meaningful results that improve infrastructure investments and ultimately opportunities for society.