Erik Csikos' 4D DAG-ness metric eliminates topological redundancy

Directed acyclic graphs (DAGs) are foundational in causal inference, neural architecture search, and hierarchical modeling — but real-world networks rarely exhibit pure acyclicity. Erik Csikos (Binghamton University & Moravian University) identifies a critical flaw in prior continuous DAG-ness measures: topological redundancy from overlapping cyclic penalties, which artificially deflates scores for networks with minor feedback (the 'Dilution Trap'). To solve this, Csikos introduces a strictly orthogonal 4-dimensional framework that independently measures feedback volume A(G), flow alignment F(G), macroscopic locality of feedback M(G), and dynamical pathway complexity S(G). Each component captures a distinct structural axis, preventing collinearity and enabling a composite score D(G) that gracefully degrades in the presence of noise or localized loops.

Empirical validation on synthetic diagnostic graphs confirms the metric's mathematical stability, while deterministic application to two classic number-theoretic systems — the Kaprekar routine graph and the Collatz conjecture graph — demonstrates the framework's ability to rigorously differentiate topological flow from dynamical entrapment. Unlike binary DAG tests, the continuous DAG-ness score scales smoothly and provides interpretable insights for systems with partial acyclicity. This work, published on arXiv (2606.22205), has immediate implications for causal structure learning, Bayesian network scoring, and automated AI pipeline design where graphs are often only approximately DAG.