The Cosine Drainage Theorem: A Rank-One Proof and a Cross-Family Conjecture for Embedded Non-Regular Graphs

Contact: [email protected]. Cosine-similarity-biased traversal of high-dimensional embedded graphs systematically fails to reach graph-reachable targets. This paper proves the Rank-One Cosine Drainage Theorem under the Chung-Lu model. Multi-Anchor expansion outperforms single-source cosine in all 15 evaluated graph families. GitHub: github.com/mjgodat/cosine-drainage-theorem

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-04
DOI
https://doi.org/10.5281/zenodo.21989590
Citations
5
Primary Topic
Advanced Graph Neural Networks
Type
article
Field-Weighted Citation Impact
31.72
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article

The Cosine Drainage Theorem: A Rank-One Proof and a Cross-Family Conjecture for Embedded Non-Regular Graphs

Michael Godat
5 citations
Zenodo (CERN European Organization for Nuclear Research)
Advanced Graph Neural Networks
31.72
article

The Cosine Drainage Theorem: A Rank-One Proof and a Cross-Family Conjecture for Embedded Non-Regular Graphs

Michael Godat
article en
5 citations

Abstract

Contact: [email protected]. Cosine-similarity-biased traversal of high-dimensional embedded graphs systematically fails to reach graph-reachable targets. This paper proves the Rank-One Cosine Drainage Theorem under the Chung-Lu model. Multi-Anchor expansion outperforms single-source cosine in all 15 evaluated graph families. GitHub: github.com/mjgodat/cosine-drainage-theorem

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 0%
Advanced Graph Neural Networks
31.72
DOIOpen Access PDFOpenAlex
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The Cosine Drainage Theorem: A Rank-One Proof and a Cross-Family Conjecture for Embedded Non-Regular Graphs — Michael Godat · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS