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Multilayer graphs are commonly used for representing different relationsbetween entities and handling heterogeneous data processing tasks. Newchallenges arise in multilayer graph clustering for assigning clusters to acommon multilayer node set and for combining information from each layer. Thispaper presents a theoretical framework for multilayer spectral graph clusteringof the nodes via convex layer aggregation. Under a novel multilayer signal plusnoise model, we provide a phase transition analysis that establishes theexistence of a critical value on the noise level that permits reliable clusterseparation. The analysis also specifies analytical upper and lower bounds onthe critical value, where the bounds become exact when the clusters haveidentical sizes. Numerical experiments on synthetic multilayer graphs areconducted to validate the phase transition analysis and study the effect oflayer weights and noise levels on clustering reliability.

Multilayer Spectral Graph Clustering via Convex Layer Aggregation