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Lumping Reductions for Multispread in Multi-Layer Networks

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Part of the Studies in Computational Intelligence book series (SCI,volume 1016)

Abstract

Spreading phenomena arise from simple local interaction among a large number of actors through different networks of interactions. Computational modelling and analysis of such phenomena is challenging due to the combinatorial explosion of possible network configurations. Traditional (single layer) networks are commonly used to encode the heterogeneous relationships among agents but are limited to a single type of interaction. Multiplex Multi-Layer networks (MLNs) have been introduced to allow the modeler to compactly and naturally describe multiple types of interactions and multiple simultaneous spreading phenomena. The downside is an increase in the complexity of the already challenging task of the analysis and simulation of such spreading processes. In this paper we explore the use of lumping techniques that preserve dynamics, previously applied to Continuous Time Markov Chains (CTMC) and single layer networks to multiple spreading processes on MLNs.

Keywords

  • Multiplex multi-layer networks
  • Spreading processes
  • Model reduction techniques
  • Lumping
  • Stochastic processes

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Notes

  1. 1.

    The algorithm is a variation of the Paige-Tarjan algorithm.

  2. 2.

    Further discussion on the choice of \(\alpha \) and \(\beta \) is beyond the scope of this manuscript and we refer the interested reader to  [18].

  3. 3.

    The code and examples are available https://github.com/stefanotognazzi/LumpingForMLNs.

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Acknowledgements

This work was supported by the Ministry of Science, Research and the Arts of the state of Baden-Württemberg, and the DFG Centre of Excellence 2117 ‘Centre for the Advanced Study of Collective Behaviour’ (ID: 422037984). The authors would like to thank Giacomo Rapisardi for the inspiring discussions on the topic and Andrea Vandin for the support and the insights on the use of the tool ERODE.

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Correspondence to Stefano Tognazzi .

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Petrov, T., Tognazzi, S. (2022). Lumping Reductions for Multispread in Multi-Layer Networks. 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 1016. Springer, Cham. https://doi.org/10.1007/978-3-030-93413-2_25

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  • DOI: https://doi.org/10.1007/978-3-030-93413-2_25

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