Directed cycles as higher-order units of information processing in complex networks
File(s)
Published version (article in press)
Author(s)
Rajpal, Hardik
Expert, Paul
Vasiliauskaite, Vaiva
Type
Journal Article
Abstract
Directed cycles are fundamental motifs in natural, social and artificial networks, yet their distinct roles in processing information remain poorly understood, particularly as higher-order structures. Furthermore, it is unclear how the function of a cycle depends on the wider network in which it is embedded. Here we show, using information-theoretic measures, that network size, sparsity and directionality critically shape how directed cycles process information. In networks with no preferred direction, feedforward cycles enable greater information flow, while feedback cycles support stronger information integration. The relative orientation of a feedforward cycle, and the structural incoherence it induces, tunes its capacity to generate higher-order behaviour. Introducing feedback into otherwise feedforward architectures increases the diversity of network activity while modifying the computational behaviour. In a supervised learning task, feedforward networks train faster and tolerate random node ablations, whereas feedback makes them robust to input noise. These findings reveal directed cycles as tunable computational units whose behaviour is set by their structural context.
Date Issued
2026-08-17
Date Acceptance
2026-08-05
Citation
Communications Physics, 2026
ISSN
2399-3650
Publisher
Nature Portfolio
Journal / Book Title
Communications Physics
Copyright Statement
© The Author(s) 2026. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Publication Status
Published online
Date Publish Online
2026-08-17