Analytical controllability of deterministic scale-free networks and Cayley trees

TL;DR

This paper analytically investigates the controllability of deterministic scale-free networks and Cayley trees, revealing their robustness to link weights and identifying minimal driver node sets.

Contribution

It provides exact controllability analysis for self-similar bipartite networks, deriving analytical results and driver node configurations based on their self-similarity.

Findings

Controllability is unaffected by link weights in these networks.

Analytical expressions for driver node sets are derived.

Results have implications for controlling real self-similar networks.

Abstract

According to the exact controllability theory, the controllability is investigated analytically for two typical types of self-similar bipartite networks, i.e., the classic deterministic scale-free networks and Cayley trees. Due to their self-similarity, the analytical results of the exact controllability are obtained, and the minimum sets of driver nodes (drivers) are also identified by elementary transformations on adjacency matrices. For these two types of undirected networks, no matter their links are unweighted or (nonzero) weighted, the controllability of networks and the configuration of drivers remain the same, showing a robustness to the link weights. These results have implications for the control of real networked systems with self-similarity.