  The connection between curvature and topology is a very well-studied theme in
the subject of differential geometry. By suitably defining curvature on
networks, the study of this theme has been extended into the domain of network
analysis as well. In particular, this has led to curvature-based community
detection algorithms. In this paper, we reveal the relation between community
structure of a network and the curvature of its edges. In particular, we give
apriori bounds on the curvature of intercommunity edges of a graph.
