With the burgeoning advancements of computing and network communication technologies, network infrastructures and their application environments have become increasingly complex. Due to the increased complexity, networks are more prone to hardware faults and highly susceptible to cyber-attacks. Therefore, for rapidly growing network-centric applications, network resilience is essential to minimize the impact of attacks and to ensure that the network provides an acceptable level of services during attacks, faults or disruptions. In this regard, this thesis focuses on developing effective approaches for enhancing network resilience. Existing approaches for enhancing network resilience emphasize on determining bottleneck nodes and edges in the network and designing proactive responses to safeguard the network against attacks. However, existing solutions generally consider broader application domains and possess limited applicability when applied to specific application areas such as cyber defense and information diffusion, which are highly popular application domains among cyber attackers. This thesis aims to design effective, efficient and scalable techniques for discovering bottleneck nodes and edges in the network to enhance network resilience in cyber defense and information diffusion application domains. We first investigate a cyber defense graph optimization problem, i.e., hardening active directory systems by discovering bottleneck edges in the network. We then study the problem of identifying bottleneck structural hole spanner nodes, which are crucial for information diffusion in the network. We transform both problems into graph-combinatorial optimization problems and design machine learning based approaches for discovering bottleneck points vital for enhancing network resilience.