We develop a graph-based method to study the entanglement entropy of Calderbank-Shor-Steane quantum codes. This method offers a straightforward interpretation for the entanglement entropy of quantum error-correcting codes through graph-theoretical concepts, shedding light on the origins of both the local and long-range entanglement. Moreover, it inspires a scheme for evaluating the entanglement entropy of arbitrary Calderbank-Shor-Steane quantum codes, which can be computationally advantageous when a simple graph representation is available. We illustrate the method by calculating the von Neumann entropy of subsystems in toric codes and two types of quantum low-density parity-check codes, and by comparing the scaling behavior of the entanglement entropy with respect to the subsystem size. Our method introduces a perspective for understanding the entanglement structure in quantum many-body systems.

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• Entanglement entropy
• Quantum error correction
• Quantum information theory