Failures in vulnerable branches can lead to a decline in the stability of regional integrated energy systems and even trigger large-scale system instability. Therefore, identifying the vulnerable branches of the system becomes a crucial step in ensuring safe and stable operation as well as prevention. To address this, a method for identifying vulnerable branches in electric-gas-thermal regional integrated energy systems is proposed. First, based on the unified energy route theory, unified energy flow modeling and calculations are performed for the electric-gas-thermal network to obtain the initial operating state of the network. At the same time, a set of hypothetical accidents for the regional integrated energy system is established, considering the impact of N-1 contingencies in the thermal and electric networks on the internal network. The post-fault operational state of the branches is then determined through N-1 analysis. Next, vulnerability analysis is conducted based on the operational characteristics of energy flow entropy changes and the structural characteristics of local concentration, and a comprehensive vulnerability index for the branches is proposed. Particle swarm optimization (PSO) is used to determine the weights of operational and structural vulnerabilities, ensuring the objectivity and accuracy of the evaluation process. The branches are then ranked according to the vulnerability index, allowing the identification of the system′s vulnerable branches. Finally, the method is applied to an IEEE 14-bus electric system, a 14-node gas network, and a 14-node thermal network to identify the vulnerable branches of the system. The experimental results show that the proposed method can reasonably reflect the actual conditions of the system, and the weights determined by the PSO algorithm can more effectively identify the vulnerable branches, improving the accuracy and reliability of the identification process.