  Many systems are naturally represented by a multilayer network in which edges
exist in multiple layers that encode different, but potentially related, types
of interactions, and it is important to understand limitations on the
detectability of community structure in these networks. Using random matrix
theory, we analyze detectability limitations for multilayer (specifically,
multiplex) stochastic block models (SBMs) in which L layers are derived from a
common SBM. We study the effect of layer aggregation on detectability for
several aggregation methods, including summation of the layers' adjacency
matrices for which we show the detectability limit vanishes as O(L^{-1/2}) with
increasing number of layers, L. Importantly, we find a similar scaling behavior
when the summation is thresholded at an optimal value, providing insight into
the common - but not well understood - practice of thresholding
pairwise-interaction data to obtain sparse network representations.
