  Multilayer graphs are commonly used for representing different relations
between entities and handling heterogeneous data processing tasks. New
challenges arise in multilayer graph clustering for assigning clusters to a
common multilayer node set and for combining information from each layer. This
paper presents a theoretical framework for multilayer spectral graph clustering
of the nodes via convex layer aggregation. Under a novel multilayer signal plus
noise model, we provide a phase transition analysis that establishes the
existence of a critical value on the noise level that permits reliable cluster
separation. The analysis also specifies analytical upper and lower bounds on
the critical value, where the bounds become exact when the clusters have
identical sizes. Numerical experiments on synthetic multilayer graphs are
conducted to validate the phase transition analysis and study the effect of
layer weights and noise levels on clustering reliability.
