The natural gas pipeline system (NGPS) is complex with a diverse network topology. This study elucidates the network characteristics of the NGPS, revealing that it shares commonalities with small-world networks, but with differences caused by its structural and operational characteristics. The combination of the low aggregation effect caused by branching structure and the offsetting effect caused by economic and geographical constraints results in a network with small world characteristics. NGPS has longer mean path than common small world network, but the aggregation factor is close to that of a standard small world network. With respect to its small-world characteristics and correlation with self-organized criticality (SOC), an in-depth study of the SOC characteristics of the NGPS was conducted utilizing a combination of traditional logarithm analysis and R/S analysis. The findings establish that there are atypical SOC characteristics, characterized by a weakened power law within a specific functional range, thereby encouraging the advancement of SCADA and other safety technologies. Because of the line-pack, which induces time lags in the NGPS, NGPS can prevent the cascade failures. The reasons for the periodicity and centrality of NGPS data are analyzed by the affecting components, with the R/S analysis verifying a weak positive correlation of the function data across different time series. The interlinking of the SOC and R/S analysis illustrates the connection between critical status, accident type, and operation index. The results prove the reasonability and importance of insurance measures, such as regular internal detection, higher grade steel pipes change and staff training et al., in a novel view of SOC. The future works in building accidents database and human factors study are proposed. © 2023 The Authors