We study layer-specific community detection in multilayer networks with heterogeneous community memberships and degree distributions. Membership mismatch complicates cross-layer information pooling, whereas sparsity heterogeneity can provide complementary signals for poorly connected communities. We recast the problem as network-with-covariates clustering: the target layer is retained as the primary network, while the remaining layers are converted into nodal covariates through our regularized spectral construction approach. We then perform community detection using a node-adaptive balancing scheme that relies more on the target network for high-degree nodes and more on the constructed covariates for low-degree nodes. Under a multilayer degree-corrected stochastic blockmodel, we establish guarantees for the constructed covariates and weak consistency when the average membership mismatch vanishes. Under additional degree structure and node-specific mismatch conditions, we establish strong consistency while allowing the average membership mismatch to remain nonvanishing. Simulations show that our proposed approach achieves the lowest misclustering error rates under most scenarios. An application to international food-trading networks reveals interpretable product-specific community structures.

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