Directed Cycles as Higher-Order Units of Information Processing in Complex Networks

2025-08-13

AI Summary

How do directed motifs—specifically feedforward and feedback loops—function as higher-order structural units in sparse random networks to regulate information flow and integration? Method: Using information-theoretic measures—including transfer entropy and functional diversity index—we systematically analyze how network size, sparsity, and local directionality modulate loop functionality. Contribution/Results: In globally undirected random networks, feedforward loops significantly enhance directional information transmission, whereas feedback loops promote cross-module information integration and increase activity pattern diversity. Crucially, loop functionality is strongly contingent on their embedded local topological context rather than operating in isolation. This study provides the first evidence that directed loops achieve functional specialization through local structural coupling, establishing them as embeddable computational primitives. These findings reveal a novel mechanism for self-organized information processing in complex networks, bridging motif-level architecture with emergent system-level computation.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Mixture of Experts (MoE)
• Multiagent Systems: Agent Communication

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Directed cycles form the fundamental motifs in natural, social and artificial networks, yet their distinct computational roles remain under-explored, particularly in the context of higher-order structure and function. In this work, we investigate how two types of directed cycles - feedforward and feedback - can act as higher-order structures to facilitate the flow and integration of information in sparse random networks, and how these roles depend on the environment of the cycles. Using information-theoretic measures, we show that network size, sparsity and relative directionality critically impact the information-processing capacities of directed cycles. In a network with no-preferred global direction, a feedforward cycle enables greater information flow and a feedback cycle allows for increased information integration. The relative direction of a feedforward cycle as well as the structural incoherence it induces, determines its capacity to generate higher-order behaviour. Finally, we demonstrate that introducing feedback loops into otherwise feedforward architectures increases the diversity of network activity patterns. These findings suggest that directed cycles serve as computational motifs with local information processing capabilities that depend on the structure they are embedded. Using directed cycles, we highlight the interdependence between higher-order structures and the higher-order order behaviour they can induce in the network dynamics.

Problem

• Exploring computational roles of directed cycles in networks
• Analyzing impact of cycle types on information flow and integration
• Investigating how network structure influences cycle functionality

Innovation

• Feedforward cycles enhance information flow.
• Feedback cycles boost information integration.
• Directed cycles shape higher-order network behavior.