Effects of adding a reverse edge across a stem in a directed acyclic graph

Abstract

Directed acyclic graphs (DAGs) widely exist in natural biological, industrial, and social networked systems. This brief 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. From the application perspective, this brief provides a guidance for an attacking (or conversely anti-attacking) strategy of injecting the most effective malicious reverse edge. It has other potential applications in regulating DAG network convergence performance with reverse edges.