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