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The extreme high temperature weather event caused by global warming has increased the risk of urban electric power supply. Critical risk determination method is useful to the system risk prevention and adaptive strategy formulation. Based on analyzing the failure mechanism of power supply under heat wave impact, the paper put forward the method framework of energy-flow network on electric power system risk evaluation. There are three parts in the framework including energy-flow chart analysis of power supply and consumption, establishment and network analysis of Gephi visualization network, and matrix diagram evaluation of node importance. The visualized network of power system with different years and electricity input from external area were established and compared in the case study of Beijing in China. The analysis results showed that the network structure stability of the power system decreased slightly, which was due to the node energy flow becoming high imbalance such as power input from external area, local power generation and energy consumption. For risk prevention, power infrastructures should focus on the high-voltage transmission and distribution facilities and 500 kV hub substations. Meanwhile, to electric power generation and supply, natural gas supply and power supply from Inner Mongolia Autonomous Region played the key roles. And power consumption should focus on the tertiary industry and living consumption. • Energy-flow chart of power system was transformed into network by Gephi. • Node importance was evaluate by matrix diagram with node degree and edge weight. • Electric power system of Beijing was analyzed and discussed. • Energy-flow imbalance of system components reduced network system stability. [ABSTRACT FROM AUTHOR]