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Topological Analysis of Temporal Hypergraphs

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Algorithms and Models for the Web Graph (WAW 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13894))

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Abstract

In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of network science. A common use of hypergraphs is to model events as hyperedges in which the event can involve many elements as nodes. This provides a more complete picture of the event, which is not limited by the standard dyadic connections of a graph. However, a common attribution to events is temporal information as an interval for when the event occurred. Consequently, a temporal hypergraph is born, which accurately captures both the temporal information of events and their multi-way connections. Common tools for studying these temporal hypergraphs typically capture changes in the underlying dynamics with summary statistics of snapshots sampled in a sliding window procedure. However, these tools do not characterize the evolution of hypergraph structure over time, nor do they provide insight on persistent components which are influential to the underlying system. To alleviate this need, we leverage zigzag persistence from the field of Topological Data Analysis (TDA) to study the change in topological structure of time-evolving hypergraphs. We apply our pipeline to both a cyber security and social network dataset and show how the topological structure of their temporal hypergraphs change and can be used to understand the underlying dynamics.

Information release number: PNNL-SA-181478.

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Notes

  1. 1.

    Notice we use “topology” here in the formal sense, as distinct from how this is used informally in graph applications to refer to connectivity patterns in networks.

  2. 2.

    HyperNetX: https://pnnl.github.io/HyperNetX.

  3. 3.

    Dionysus2: https://mrzv.org/software/dionysus2/.

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Author information

Authors and Affiliations

  1. Pacific Northwest National Laboratory, Mathematics of Data Science, Richland, USA

    Audun Myers, Cliff Joslyn, Emilie Purvine, Gregory Roek & Madelyn Shapiro

  2. Pacific Northwest National Laboratory, Computational Mathematics, Richland, USA

    Bill Kay

Authors
  1. Audun Myers
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  2. Cliff Joslyn
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  3. Bill Kay
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  4. Emilie Purvine
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  5. Gregory Roek
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  6. Madelyn Shapiro
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Corresponding author

Correspondence to Audun Myers .

Editor information

Editors and Affiliations

  1. Tutte Institute for Mathematics and Computing, Ottawa, ON, Canada

    Megan Dewar

  2. Toronto Metropolitan University, Toronto, ON, Canada

    Paweł Prałat

  3. SGH Warsaw School of Economics, Warsaw, Poland

    Przemysław Szufel

  4. Tutte Institute for Mathematics and Computing, Ottawa, ON, Canada

    François Théberge

  5. SGH Warsaw School of Economics, Warsaw, Poland

    Małgorzata Wrzosek

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Myers, A., Joslyn, C., Kay, B., Purvine, E., Roek, G., Shapiro, M. (2023). Topological Analysis of Temporal Hypergraphs. In: Dewar, M., Prałat, P., Szufel, P., Théberge, F., Wrzosek, M. (eds) Algorithms and Models for the Web Graph. WAW 2023. Lecture Notes in Computer Science, vol 13894. Springer, Cham. https://doi.org/10.1007/978-3-031-32296-9_9

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  • DOI: https://doi.org/10.1007/978-3-031-32296-9_9

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