  Detecting significant community structure in networks with incomplete
observations is challenging because the evidence for specific solutions fades
away with missing data. For example, recent research shows that flow-based
community detection methods can highlight spurious communities in sparse
undirected and unweighted networks with missing links. Current Bayesian
approaches developed to overcome this problem do not work for incomplete
observations in weighted and directed networks that describe network flows. To
address this gap, we extend the idea behind the Bayesian estimate of the map
equation for unweighted and undirected networks to enable more robust community
detection in weighted and directed networks. We derive a weighted and directed
prior network that can incorporate metadata information and show how an
efficient implementation in the community-detection method Infomap provides
more reliable communities even with a significant fraction of data missing.
