Abstract Let D be a digraph with set of vertices V ( D ) and set of arcs A ( D ). Recently, the Randić index of D was extended to digraphs as urn:x-wiley:00207608:media:qua26744:qua26744-math-0001 where and are the out‐degree and in‐degree of u and v , respectively. In this paper we study the extremal values of R over the set of all orientations of hexagonal chains with k hexagons.