Abstract

Abundant directed acyclic graphs (DAGs) exist in natural biological, industrial, and social networked systems like hierarchical fish schools, bird flocks and human social societies. This paper explores the effects of adding a reverse edge, across a so-called stem, in a DAG on consensus performance. In particular, it quantitatively reveals the effects in terms of the in-degrees of the surpassed stem nodes. The study further enriches the existing results on special chain and grid networks by accommodating more general network topologies arising in natural, engineering, and social DAGs. The study is also beneficial for regulating the convergence rate of a DAG with reverse edges by tuning in-degrees of the stem nodes.