  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. 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 exploring the monotonicity
property of the Laplacian eigenvectors, a neighbor selection rule with
guaranteed performance enhancements, can be realized for consensus-type
networks. For distributed implementation, a quantitative connection between
entries of 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.
