Distributed Neighbor Selection on Matrix-weighted Networks

This paper explores distributed neighbor selection in matrix-weighted networks, where a matrix-valued weight captures the interdependencies among agents’ states. We demonstrate the feasibility of preserving and, in certain cases, improving the convergence rate of matrix-weighted networks by having agents exclusively engage with a subset of their neighbors. Leveraging the inherent monotonicity of Laplacian matrix eigenvectors, we introduce a novel neighbor selection criterion that reduces network connections while enhancing convergence rates. Existing neighbor selection strategies often require acquiring information from all nodes before making decisions. In order to propose a distributed neighbor selection strategy for matrix-weighted networks, we establish a numerical relationship between Laplacian eigenvectors and a locally measurable metric. In essence, this paper extends prior findings from scalar-weighted networks to matrix-weighted networks.