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Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems

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Matrix-based pagerank control in hypergraphs for semantic text summaries.

David Aleja^1,2,3, Regino Criado^1,2,3, Ángeles Criado-Alonso⁴

¹Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, Universidad Rey Juan Carlos, C/Tulipán s/n, 28933, Móstoles, Madrid, Spain.

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|December 15, 2025

Summary

This summary is machine-generated.

We introduce a new method for analyzing random walks on hypergraphs using labeled multidigraphs. This approach allows for better control over walker behavior and generalizes restrictions like non-backtracking for diverse applications.

Keywords:

Document summarization Higher order network Hypergraph Linguistic patterns PageRank on hypergraphs

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Area of Science:

Graph Theory
Hypergraph Theory
Computational Linguistics

Background:

Random walks are fundamental in analyzing graph structures.
Hypergraphs offer a more general framework for representing complex relationships.
Existing methods for random walks on hypergraphs have limitations in control and analysis.

Purpose of the Study:

To develop a novel framework for describing random walks on hypergraphs.
To enable intrinsic analysis and control of random walker behavior.
To generalize restrictions on random walks, such as non-backtracking.

Main Methods:

Utilizing a labeled multidigraph representation for hypergraphs.
Employing a special decomposition of the frequency matrix of relations.
Incorporating memory and walk restrictions at the matrix level.

Main Results:

A novel description of random walks in hypergraphs is presented.
The decomposition method allows for intrinsic analysis and control of walker behavior.
The non-back-tracking restriction is generalized, enabling broader applicability.

Conclusions:

The proposed framework offers enhanced control and analysis of random walks on hypergraphs.
This method has direct applications in natural language processing tasks like document summarization.
The generalized non-backtracking restriction opens new avenues for research and application.