Representation of a word by a graph is an important branch of study in combinatorics of words. The vertices and the edges are defined using certain properties of words. Such a representation is useful in solving some problems in graph theory. One such representation is the idea of Rauzy graphs that was used to study Arnoux-Rauzy sequences. In this paper, we define half range Rauzy graphs and study the structural properties of such a variant for some special words. © 2018 Editura Academiei Romane. All rights reserved.