Distributed Neighbor Selection in Multi-agent Networks

Achieving consensus via nearest neighbor rules is an important prerequisite for multi-agent networks to accomplish collective tasks. A common assumption in consensus setup is that each agent interacts with all its neighbors during the process. This paper examines whether network functionality and performance can be maintained-and even enhanced-when agents interact only with a subset of their respective (available) neighbors. As shown in the paper, the answer to this inquiry is affirmative. In this direction, we show that by using the monotonicity property of the Laplacian eigenvectors, a neighbor selection rule with guaranteed performance enhancements, can be realized for consensus-type networks. For the purpose of distributed implementation, a quantitative connection between Laplacian eigenvectors and the "relative rate of change" in the state between neighboring agents is further established; this connection facilitates a distributed algorithm for each agent to identify "favorable" neighbors to interact with. Multi-agent networks with and without external influence are examined, as well as extensions to signed networks. This paper underscores the utility of Laplacian eigenvectors in the context of distributed neighbor selection, providing novel insights into distributed data-driven control of multi-agent systems.