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Semi-Markov Graph Dynamics

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  • Marco Raberto
  • Fabio Rapallo
  • Enrico Scalas

Abstract

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.

Suggested Citation

  • Marco Raberto & Fabio Rapallo & Enrico Scalas, 2011. "Semi-Markov Graph Dynamics," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    • Handle: RePEc:plo:pone00:0023370
    DOI: 10.1371/journal.pone.0023370
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    Cited by:

    1. Cristiano Bocci & Luca Chiantini & Fabio Rapallo, 2014. "Max-Plus Objects to Study the Complexity of Graphs," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 507-525, September.
    2. Scalas, Enrico & Rapallo, Fabio & Radivojević, Tijana, 2017. "Low-traffic limit and first-passage times for a simple model of the continuous double auction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 61-72.
    3. Diego Aparicio & Daniel Fraiman, 2015. "Banking Networks And Leverage Dependence In Emerging Countries," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(07n08), pages 1-21, November.
    4. Meerschaert, Mark M. & Toaldo, Bruno, 2019. "Relaxation patterns and semi-Markov dynamics," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2850-2879.

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