Random graph ensembles with many short loops

ES Roberts; ACC Coolen

doi:10.1051/proc/201447006

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Random graph ensembles with many short loops

ES Roberts ^1,² ; ACC Coolen ^1,³

¹ Institute for Mathematical and Molecular Biomedicine, King’s College London, Hodgkin Building, London SE1 1UL, United Kingdom
² Randall Division of Cell and Molecular Biophysics, King’s College London, New Hunts House, London SE1 1UL, United Kingdom
³ London Institute for Mathematical Sciences, 35a South St, Mayfair, London W1K 2XF, United Kingdom

ESAIM. Proceedings, Tome 47 (2014), pp. 97-115.

Voir la notice de l'article provenant de la source EDP Sciences

Résumé

Networks observed in the real world often have many short loops. This violates the tree-like assumption that underpins the majority of random graph models and most of the methods used for their analysis. In this paper we sketch possible research routes to be explored in order to make progress on networks with many short loops, involving old and new random graph models and ideas for novel mathematical methods. We do not present conclusive solutions of problems, but aim to encourage and stimulate new activity and in what we believe to be an important but under-exposed area of research. We discuss in more detail the Strauss model, which can be seen as the ‘harmonic oscillator’ of ‘loopy’ random graphs, and a recent exactly solvable immunological model that involves random graphs with extensively many cliques and short loops.

DOI : 10.1051/proc/201447006

Affiliations des auteurs :

ES Roberts ^{1, 2} ; ACC Coolen ^{1, 3}

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     author = {ES Roberts and ACC Coolen},
     title = {Random graph ensembles with many short loops},
     journal = {ESAIM. Proceedings},
     pages = {97--115},
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     volume = {47},
     year = {2014},
     doi = {10.1051/proc/201447006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201447006/}
}

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ES Roberts; ACC Coolen. Random graph ensembles with many short loops. ESAIM. Proceedings, Tome 47 (2014), pp. 97-115. doi : 10.1051/proc/201447006. http://geodesic.mathdoc.fr/articles/10.1051/proc/201447006/

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