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Max-Plus Objects to Study the Complexity of Graphs

Author

Listed:
  • Cristiano Bocci

    (Università di Siena)

  • Luca Chiantini

    (Università di Siena)

  • Fabio Rapallo

    (Università del Piemonte Orientale)

Abstract

Given an undirected graph G, we define a new object H G , called the mp-chart of G, in the max-plus algebra. We use it, together with the max-plus permanent, to describe the complexity of graphs. We show how to compute the mean and the variance of H G in terms of the adjacency matrix of G and we give a central limit theorem for H G . Finally, we show that the mp-chart is easily tractable also for the complement graph.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:3:d:10.1007_s11009-012-9311-x
    DOI: 10.1007/s11009-012-9311-x
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    References listed on IDEAS

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    4. Marco Raberto & Fabio Rapallo & Enrico Scalas, 2011. "Semi-Markov Graph Dynamics," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    5. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
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