  Network structure plays a critical role in functionality and performance of
network systems. This paper examines structural adaptivity of diffusively
coupled, directed multi-agent networks that are subject to diffusion
performance. Inspired by the observation that the link redundancy in a network
may degrade its diffusion performance, a distributed data-driven neighbor
selection framework is proposed to adaptively adjust the network structure for
improving the diffusion performance of exogenous influence over the network.
Specifically, each agent is allowed to interact with only a specific subset of
neighbors while global reachability from exogenous influence to all agents of
the network is maintained. Both continuous-time and discrete-time directed
networks are examined. For each of the two cases, we first examine the
reachability properties encoded in the eigenvectors of perturbed variants of
graph Laplacian or SIA matrix associated with directed networks, respectively.
Then, an eigenvector-based rule for neighbor selection is proposed to derive a
reduced network, on which the diffusion performance is enhanced. Finally,
motivated by the necessity of distributed and data-driven implementation of the
neighbor selection rule, quantitative connections between eigenvectors of the
perturbed graph Laplacian and SIA matrix and relative rate of change in agent
state are established, respectively. These connections immediately enable a
data-driven inference of the reduced neighbor set for each agent using only
locally accessible data. As an immediate extension, we further discuss the
distributed data-driven construction of directed spanning trees of directed
networks using the proposed neighbor selection framework. Numerical simulations
are provided to demonstrate the theoretical results.
