Node failures have a terrible effect on the connectivity of the network. In traditional models, the failures of nodes affect their neighbors and may further trigger the failures of their neighbors, and so on. However, it is also possible that node failures would indirectly cause the failure of nodes that are not adjacent to the failed one. In a power grid, generators share the load. Failure of one generator induces extra load on other generators in the network, which could further trigger their failures. We call such failures causal failures. In this dissertation, we consider the impact of causal failures on multiple aspects of one network. More specifically, we list the content as follows. • In Chapter 1, we introduce basic concepts of networks and graphs, classical models of failures and formally define causal failures in a given network. • Chapter 2 addresses the network’s robustness and aims to find the maximum number of causal failures while maintaining a connected component with a size of at least a given integer. More specifically, we are looking into the number of causal node failures we can tolerate yet have most of the system connected with α being used to parametrize. • Chapter 3 deals with vulnerability, wherein we aim to find the minimum number of causal failures such that there are at least k connected components remaining. We are looking for the set of causal failures that will result in the network being disconnected into k or more components. • In Chapter 4, we consider causal node failures occurring in a cascading manner. Cascading causal node failures affect communication within nodes, which is dependent on the paths that connect them. Therefore, in this context of the cascading causal failure model, we study the impact of cascading causal failures on the distance between a pair of nodes in the network. More precisely, given a network G, a set of causal failures (containing possible cascading failures), a pair of nodes s and t, and a constant α ≥ 1, we would like to determine the maximum number of causal failures that can be applied (meaning that the nodes in the causal failures are removed), such that in the resulting network G′, dG′ (s, t) ≤ α × dG(s, t), where dG(s, t) and dG′ (s, t) are the distance between nodes s and t in the networks G and G′, respectively. • In Chapter 5, we consider causal edge failures in flow networks and investigate the impact of causal edge failures on flow transmission. We formulate an optimization problem to find the maximum number of causal edge failures after which the flow network can still deliver d units from source node s to terminal node t. • In Chapter 6, we consider edge-weighted network augmentation when facing causal failures. We look for a set of edges with minimum weight such that the network maintains an α-giant component when applying each causality individually. We show that the optimization problems in these chapters are NP-hard and provide the corresponding mixed integer linear programming models. Moreover, we design polynomial-time heuristic algorithms to solve them approximately. In each chapter, we run experiments on multiple synthetic and real networks to compare the performance of the mixed integer linear programming models and the heuristic algorithms. The results show that the heuristic algorithms show their efficacy and efficiency compared to the mixed-integer linear programming models.