  Applied network science often involves preprocessing network data before
applying a network-analysis method, and there is typically a theoretical
disconnect between these steps. For example, it is common to aggregate
time-varying network data into windows prior to analysis, and the tradeoffs of
this preprocessing are not well understood. Focusing on the problem of
detecting small communities in multilayer networks, we study the effects of
layer aggregation by developing random-matrix theory for modularity matrices
associated with layer-aggregated networks with $N$ nodes and $L$ layers, which
are drawn from an ensemble of Erd\H{o}s-R\'enyi networks. We study phase
transitions in which eigenvectors localize onto communities (allowing their
detection) and which occur for a given community provided its size surpasses a
detectability limit $K^*$. When layers are aggregated via a summation, we
obtain $K^*\varpropto \mathcal{O}(\sqrt{NL}/T)$, where $T$ is the number of
layers across which the community persists. Interestingly, if $T$ is allowed to
vary with $L$ then summation-based layer aggregation enhances small-community
detection even if the community persists across a vanishing fraction of layers,
provided that $T/L$ decays more slowly than $ \mathcal{O}(L^{-1/2})$. Moreover,
we find that thresholding the summation can in some cases cause $K^*$ to decay
exponentially, decreasing by orders of magnitude in a phenomenon we call
super-resolution community detection. That is, layer aggregation with
thresholding is a nonlinear data filter enabling detection of communities that
are otherwise too small to detect. Importantly, different thresholds generally
enhance the detectability of communities having different properties,
illustrating that community detection can be obscured if one analyzes network
data using a single threshold.

Social and Information Networks;Physics and Society