This paper proposes two-dimensional directed graphs (or digraphs for short) as a promising alternative to the popular 2D mesh topology for networks-onchip (NoCs). Mesh is the most popular topology for the NoCs, mainly due to its suitability for on-chip implementation and low cost. However, the fact that a digraph offers a lower diameter than its equivalent linear array of equal cost motivated us to evaluate digraphs as the underlying topology of NoCs. This paper introduces a family of NoC topologies based on three well-known digraphs, namely de Bruijn, shuffleexchange, and Kautz. We study topological properties of the proposed topologies. We show that the proposed digraph-based topologies have several attractive features including constant node degree, low diameter and cost, and low zero load latency which result in superior performance over the mesh. We introduce a deadlock-free routing algorithm for the proposed NoC topologies and compare NoCs employing the proposed topologies and the mesh topology in terms of power consumption and 2 R. Sabbaghi-Nadooshan et al.performance. Simulation results also reveal that the proposed NoC topologies offer higher performance and consume lower power than the mesh NoC.