Distributed Topology Reconfiguration for Open Multiagent Systems via Algebraic Connectivity and Kirchhoff Index

This study proposes a distributed topology reconfiguration protocol for open multiagent systems (MASs) subject to dynamic agent entries and exits. Traditional greedy strategies that maximize algebraic connectivity via the Fiedler vector are limited by their myopic nature and tendency to trap the network in structurally imbalanced local optima. To address these shortcomings, the Kirchhoff index is introduced as a complementary global metric, and a unified network improvement index (UNII) is formulated to balance local connectivity gains with global structural robustness. Equipped with distributed spectral estimation algorithms, the UNII protocol enables fully decentralized decision-making for both agent entry and network repair. Simulation results confirm that the proposed method consistently constructs topologies with higher algebraic connectivity and improved robustness compared to benchmark strategies across diverse dynamic scenarios. Furthermore, application of the proposed protocol to the cooperative control of heterogeneous Euler-Lagrange systems shows that it reduces the steady-state mean squared error by several orders of magnitude and accelerates recovery from structural faults, thereby validating its feasibility as an effective and scalable solution for dynamic open-topology environments.