  Multi-view data arises frequently in modern network analysis e.g. relations
of multiple types among individuals in social network analysis, longitudinal
measurements of interactions among observational units, annotated networks with
noisy partial labeling of vertices etc. We study community detection in these
disparate settings via a unified theoretical framework, and investigate the
fundamental thresholds for community recovery. We characterize the mutual
information between the data and the latent parameters, provided the degrees
are sufficiently large. Based on this general result, (i) we derive a sharp
threshold for community detection in an inhomogeneous multilayer block model
\citep{chen2022global}, (ii) characterize a sharp threshold for weak recovery
in a dynamic stochastic block model \citep{matias2017statistical}, and (iii)
identify the limiting mutual information in an unbalanced partially labeled
block model. Our first two results are derived modulo coordinate-wise convexity
assumptions on specific functions -- we provide extensive numerical evidence
for their correctness. Finally, we introduce iterative algorithms based on
Approximate Message Passing for community detection in these problems.
