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On the likelihood of forests

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  • Shang, Yilun

Abstract

How complex a network is crucially impacts its function and performance. In many modern applications, the networks involved have a growth property and sparse structures, which pose challenges to physicists and applied mathematicians. In this paper, we introduce the forest likelihood as a plausible measure to gauge how difficult it is to construct a forest in a non-preferential attachment way. Based on the notions of admittable labeling and path construction, we propose algorithms for computing the forest likelihood of a given forest. Concrete examples as well as the distributions of forest likelihoods for all forests with some fixed numbers of nodes are presented. Moreover, we illustrate the ideas on real-life networks, including a benzenoid tree, a mathematical family tree, and a peer-to-peer network.

Suggested Citation

  • Shang, Yilun, 2016. "On the likelihood of forests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 157-166.
    • Handle: RePEc:eee:phsmap:v:456:y:2016:i:c:p:157-166
    DOI: 10.1016/j.physa.2016.03.021
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    References listed on IDEAS

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    1. Fragkiskos Papadopoulos & Maksim Kitsak & M. Ángeles Serrano & Marián Boguñá & Dmitri Krioukov, 2012. "Popularity versus similarity in growing networks," Nature, Nature, vol. 489(7417), pages 537-540, September.
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    Cited by:

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    2. Claudia Angelini & Daniela De Canditiis & Anna Plaksienko, 2021. "Jewel : A Novel Method for Joint Estimation of Gaussian Graphical Models," Mathematics, MDPI, vol. 9(17), pages 1-24, August.

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