Encoding Impact of Network Modification on Controllability via Edge Centrality Matrix

This article develops tools to quantify the importance of agent interactions and its impact on global performance metrics for networks with scalar states modeled as linear time-invariant systems. We consider Gramian-based propose a novel notion edge centrality that encodes first-order variation in metric respect modification corresponding weight, including those edges not present network. The proposed matrix (ECM) is additive over set inputs, i.e., it captures specific contribution each edge’s presence any given actuator. provide full characterization ECM structure class directed stem-bud networks, showing nonzero entries are only possible at sub/super-diagonals determined by network size length bud. also bounds value trace, trace inverse, log-det Gramian before after single-edge modifications, edge-modification weight ensure modified retains stability. Simulations show utility validate our results.