The non-Hermitian skin effect (NHSE) has prominently emerged in non-Hermitian systems, leading to a plethora of unique features without Hermitian counterparts. However, the characterization of NHSE in many-body dynamics remains elusive. Here we present an algebraic framework to comprehensively characterize the entanglement entropy and correlation of the steady state in many-body dynamics in the presence of the NHSE, with the methods from graph theory. We show that the NHSE can induce nontrivial correlation clustering in the many-body steady state. By interpreting pairwise mutual information or correlation in the steady state as a weighted graph, we reveal latent community structures. The quantum criticality associated with the NHSE is well captured by analyzing the modularity and centrality of the correlation network extracted from the steady state. We verify our approach by the application to several prototypical models, and successfully reproduce the phase diagrams. Our work suggests a direct and universal characterization of the long-time many-body dynamics, and offers an alternative perspective of studying the NHSE in non-Hermitian systems.

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• Network structure
• Open quantum systems
• Skin effect
• Topological phases of matter
• Non-Hermitian systems
• Nonequilibrium systems
• Quantum many-body systems
• Topology