Controlling complex networks by path cover

School of Mathematics and Statistics, Minnan Normal University - Zhangzhou 363000, China

Received: 15 October 2025
Accepted: 27 February 2026

Abstract

With the rapid development of complex networks, their effective control has attracted widespread attention. To ensure controllability, it is necessary not only to identify driver nodes but also to determine an exact input matrix. In this paper, a method based on path cover is proposed to derive an exact input matrix that satisfies the Kalman rank condition for complex networks. By assigning sufficiently large edge strength to each path in the cover, the network becomes controllable through this input matrix. The method is applicable to complex networks that are directed or undirected, weighted or unweighted. For directed networks, controllability is ensured by controlling only the source nodes of each path. In contrast, for undirected networks, it suffices to control either the source or endpoint nodes within each identified path cover. Consequently, the resulting input matrix is simple and practical for implementation.