  We currently witness the emergence of interesting new network topologies
optimized towards the traffic matrices they serve, such as demand-aware
datacenter interconnects (e.g., ProjecToR) and demand-aware overlay networks
(e.g., SplayNets). This paper introduces a formal framework and approach to
reason about and design such topologies. We leverage a connection between the
communication frequency of two nodes and the path length between them in the
network, which depends on the entropy of the communication matrix. Our main
contribution is a novel robust, yet sparse, family of network topologies which
guarantee an expected path length that is proportional to the entropy of the
communication patterns.
