Disaster resilience is a recently emerging concept, which describes a system’s overall ability to handle risks caused by disastrous events. Recently, a system-reliability-based framework of disaster resilience analysis was proposed for appropriate and reliable resilience evaluations of civil infrastructure systems (Lim et al., 2022). The framework considers uncertainties in the post-disaster states of components and their interdependencies using a diagram of pairs of reliability index (β) and redundancy index (Π), which respectively quantify the likelihood of each initial disruption scenario and the corresponding system failure probability. In this paper we apply the framework to lifeline networks to examine its application potential at the corresponding scale. In particular, a systematic methodology to evaluate the relative importance of the network components in the context of system-reliability-based disaster resilience is proposed. The method is demonstrated by applications to system reliability analysis of network connectivity, which is considered a top priority of many infrastructure networks to secure evacuations or material transmission routes in a post-disaster situation. The results confirm that the proposed method can evaluate relative component importance regarding the disaster resilience of the network with balanced considerations of network topology and component reliabilities. The proposed methodology can provide a theoretical basis for optimal decision-making strategies regarding disaster-resilience-based repairs and retrofits of network components.