Toward Structural Controllability and Predictability in Directed Networks

TL;DR

This paper explores how critical links in directed networks influence both their controllability and predictability, revealing a universal pattern and providing insights for improved control and prediction strategies.

Contribution

It demonstrates the dual role of critical links in network controllability and predictability, bridging two research fields and suggesting new control and prediction approaches.

Findings

Critical links affect network controllability and predictability.

The fraction and position of critical links influence prediction performance.

Link centrality explains the impact of critical links on network behavior.

Abstract

The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two seemingly unrelated subjects, are revealed in this paper to be both highly dependent on the critical links previously thought to only be able to influence the number of driver nodes in controllable directed networks. Here, we show that critical links can not only contribute to structural controllability, but they can also have a significant impact on the structural predictability of networks, suggesting the universal pattern of structural reciprocity in directed networks. In addition, it is shown that the fraction and location of critical links have a strong influence on the performance of prediction algorithms. Moreover, these empirical results are interpreted by introducing the link centrality based on corresponding line graphs. This work bridges the gap between the two independent research fields, and it provides indications of developing advanced control strategies and prediction algorithms from a microscopic perspective.