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The aim is to develop a continuous measure of DAG-ness to enhance understanding of directed acyclic graphs.

Quantifying DAG-ness: A Multi-Component Framework

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The aim is to develop a continuous measure of DAG-ness to enhance understanding of directed acyclic graphs.
Introduced a framework with five components to measure DAG-ness.
Analyzed edge acyclicity, node cyclicity, macro cyclicity, hierarchical flow, and spectral recurrence.
Applied the framework to five synthetic graphs to demonstrate its effectiveness.
The new measure can distinguish between graphs with varying degrees of directedness and acyclicity.
The characterization of DAG-ness uncovers important structural features that binary classifications overlook.

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Framework quantifies DAG-ness in synthetic graphs, suggesting new interpretations of graph structures.

Erik Csikos (2026) studied this question.

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