When does a digraph admit a doubly stochastic adjacency matrix?

Digraphs with doubly stochastic adjacency matrices play an essential role in a variety of cooperative control problems including distributed averaging, optimization, and gossiping. In this paper, we fully characterize the class of digraphs that admit an edge weight assignment that makes the digraph adjacency matrix doubly stochastic. As a by-product of our approach, we also unveil the connection between weight-balanced and doubly stochastic adjacency matrices. Several examples illustrate our results.