Self-stabilization is a general paradigm that characterizes the ability of a distributed system to recover from transient faults. Since its introduction by Dijkstra in 1974, self-stabilization has been successfully applied to efficiently solve many networking tasks. However, most of the literature focuses on bidirectional networks. Now, in today's networks such as WSNs, some communication channels may be one-way only. Considering such network topologies, a.k.a. directed graphs, makes self-stabilization more complicated, and sometimes even impossible. In this paper, we investigate the gap in terms of requirements and efficiency when considering a directed graph instead of an undirected one as network topology for a self-stabilizing algorithm. Our case study is a variant of a synchronous unison algorithm proposed by Arora et al.; the synchronous unison being a clock synchronization problem.