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Hypergraph Laplacians in Diffusion Framework

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Complex Networks & Their Applications X (COMPLEX NETWORKS 2021)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1073))

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Abstract

Modeling diffusion on networks is an important concept in network science. It helps to understand how an idea, information, or infection, diffuses within the network. The graph Laplacian has been used to model diffusion on graphs for years. Extending graph Laplacians to hypergraphs is not an intuitive task since hyperedges can include more than two vertices, and edge incidence and vertex adjacency are set-valued in hypergraphs. To handle this issue, researchers limit their attention to specific hypergraphs, which is often not the case for real-world hypergraphs, or reduce hypergraphs to graphs, where these reductions result in information loss. In this paper, we present two new hypergraph Laplacians that can be defined on any hypergraphs. Our Laplacians take the relations between hyperedges into consideration, hence can be used to model diffusion on hypergraphs not only between vertices but also hyperedges. As an application, we study the Enron network and show the effectiveness of the proposed Laplacians in the influential node detection problem. These Laplacians can be further employed in different hypergraph mining problems, such as social contagion models on hypergraphs, influence study on hypergraphs, hypergraph classification, and hypergraph representation learning.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Central Oklahoma, Edmond, OK, 73034, USA

    Mehmet Emin Aktas

  2. Department of Computer Science, Oklahoma State University, Stillwater, OK, 74078, USA

    Esra Akbas

Authors
  1. Mehmet Emin Aktas
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  2. Esra Akbas
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Correspondence to Mehmet Emin Aktas .

Editor information

Editors and Affiliations

  1. Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas Universidad Politécnica de Madrid, Universidad Politécnica de Madrid, Madrid, Madrid, Spain

    Rosa Maria Benito

  2. IUT Lumière, University of Lyon, Bron Cedex, France

    Chantal Cherifi

  3. LE2I, UFR Sciences et Techniques, University of Burgundy, Dijon, France

    Hocine Cherifi

  4. Grupo Interdisciplinar de Sistemas Compl, Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Center for Complex Networks and Systems Research School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Luis M. Rocha

  6. Department of Chemical Engineering, Universitat Rovira i Virgili, Tarragona, Tarragona, Spain

    Marta Sales-Pardo

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Aktas, M.E., Akbas, E. (2022). Hypergraph Laplacians in Diffusion Framework. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications X. COMPLEX NETWORKS 2021. Studies in Computational Intelligence, vol 1073. Springer, Cham. https://doi.org/10.1007/978-3-030-93413-2_24

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  • DOI: https://doi.org/10.1007/978-3-030-93413-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-93412-5

  • Online ISBN: 978-3-030-93413-2

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