Mapping the DAG-ness Landscape: Structural Archetypes in Complex Networks
Social and Information Networks
Summary
The authors studied many different directed networks, like biological and social systems, and found that just calling them 'DAG' or 'not DAG' misses important details. They used a new method called DAG-ness to measure how much these networks have certain flow and cycle properties. Their results showed that networks from very different fields surprisingly share four common structural types. This means that even complex systems with feedback often have some hierarchical, acyclic organization. The authors suggest their approach helps us better understand network structures across many domains.
Authors
Erik Csikos
Abstract
Directed networks arise across biological, social, informational, and engineered systems, yet most analyses treat directedness as a binary property: a network is either a directed acyclic graph (DAG) or it is not. This binary classification obscures the rich spectrum of hierarchical, recurrent, and modular structure present in real systems. In this paper, we empirically evaluate the DAG-ness framework, a four-component measure that quantifies acyclicity, flow alignment, cyclic locality, and pathway complexity across a corpus of 107 networks drawn from twelve structurally diverse domains. Rather than aligning with traditional disciplinary boundaries, our results reveal unexpected cross-domain convergence: diverse systems resolve into four universal structural archetypes. We find that macroscopic acyclicity is pervasive even in feedback-rich systems, and that domains as disparate as neural connectomes and abstract informational networks frequently converge on identical topological constraints. These findings demonstrate that DAG-ness provides a unified, interpretable, and domain-agnostic lens for understanding the hidden laws of directed structure in complex systems.