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Reliability evaluation is essential for the planning, operation, and analysis of community integrated energy systems (CIESs). However, it is still challenging to quantify the reliability of CIESs accurately and efficiently because of the diverse energy characteristics and energy conversion relationships. In this paper, a reliability evaluation method for CIESs based on fault incidence matrix (FIM) is proposed to analytically demonstrate the impact of equipment failures on system energy supply. The energy-bus-based unified reliability evaluation model of CIESs is presented to describe the energy flows of the system in a unified matrix form. Three types of FIMs are constructed to reveal the different consequences of device failures on energy supply. The reliability indices of a CIES can be directly calculated through simple algebraic and Boolean operations based on the FIMs, improving the calculation efficiency significantly. The FIMs make it easy to identify the vulnerability segments of the system, which is desirable in the practice of device maintenance or upgrade to improve the reliability of the CIES. Case studies are conducted on a typical CIES to verify the effectiveness and feasibility of the proposed method.