The aim of this study is to investigate the impact of network characteristics on supply chain network resilience (SCNR) when risk propagation occurs in supply chain networks (SCNs). The network characteristics we study here (e.g., clustering coefficient, scalar index, node type, etc.) are exceptionally important for real-life SCNs, but are not sufficiently considered in the previous research on SCNR. To this end, we first construct an SCN model with adjustable parameters for multiple network characteristics. Second, this SCN model is combined with a susceptible–infectious–susceptible model to construct an SCN risk propagation model. Third, we propose using the average (i.e., a novel SCNR metric considering node type) of the sizes of the maximum connected subgraphs (which contain all node types) over a period of time after risk propagation reaches a steady state. Fourth, the parameters of the SCN model are adjusted to generate SCNs with different network characteristics, and then the resilience of these SCNs is addressed accordingly. The simulation results mainly show the following: the larger the scalar index of an SCN is, the higher its resilience; the larger the clustering coefficient of an SCN is, the smaller its resilience; and the more uniform the distribution of node types is in an SCN, the higher its resilience. Our research work will help optimize SCNs’ structure, which has important implications for society and practice.