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Eigenvalues of Random Signed Graphs with Cycles: A Graph-Centered View of the Method of Moments with Practical Applications


Aceituno, Pau Vilimelis (2022). Eigenvalues of Random Signed Graphs with Cycles: A Graph-Centered View of the Method of Moments with Practical Applications. In: Benito, Rosa Maria; Cherifi, Chantal; Cherifi, Hocine; Moro, Esteban; Rocha, Luis M; Sales-Pardo, Marta. COMPLEX NETWORKS 2021: Complex Networks & Their Applications X. Cham: Springer, 390-400.

Abstract

We illustrate a simple connection between the cycles in a graph and eigenvalues its the adjacency matrix. Then we use this connection to derive properties of the eigenvalues of random graphs with short cyclic motifs and circulant graphs with random signs. We find that the eigenvalue distributions that emerge from those structures are surprisingly beautiful. Finally, we illustrate their practical relevance in the field Reservoir Computing.

Abstract

We illustrate a simple connection between the cycles in a graph and eigenvalues its the adjacency matrix. Then we use this connection to derive properties of the eigenvalues of random graphs with short cyclic motifs and circulant graphs with random signs. We find that the eigenvalue distributions that emerge from those structures are surprisingly beautiful. Finally, we illustrate their practical relevance in the field Reservoir Computing.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Scopus Subject Areas:Physical Sciences > Artificial Intelligence
Language:English
Date:1 January 2022
Deposited On:28 Mar 2022 13:37
Last Modified:27 Apr 2024 01:36
Publisher:Springer
Series Name:Studies in Computational Intelligence
ISSN:1860-949X
ISBN:9783030934125
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/978-3-030-93413-2_33
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