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Exactly solvable random graph ensemble with extensively many short cycles

Lopez, FA; Barucca, P; Fekom, M; Coolen, ACC; (2018) Exactly solvable random graph ensemble with extensively many short cycles. Journal of Physics A: Mathematical and Theoretical , 51 (8) , Article 085101. 10.1088/1751-8121/aaa555. Green open access

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Abstract

We introduce and analyse ensembles of 2-regular random graphs with a tuneable distribution of short cycles. The phenomenology of these graphs depends critically on the scaling of the ensembles' control parameters relative to the number of nodes. A phase diagram is presented, showing a second order phase transition from a connected to a disconnected phase. We study both the canonical formulation, where the size is large but fixed, and the grand canonical formulation, where the size is sampled from a discrete distribution, and show their equivalence in the thermodynamical limit. We also compute analytically the spectral density, which consists of a discrete set of isolated eigenvalues, representing short cycles, and a continuous part, representing cycles of diverging size.

Type: Article
Title: Exactly solvable random graph ensemble with extensively many short cycles
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1751-8121/aaa555
Publisher version: http://doi.org/10.1088/1751-8121/aaa555
Language: English
Additional information: © 2018 IOP Publishing Ltd. This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Physics, Multidisciplinary, Physics, Mathematical, Physics, random graph ensembles, clustering, cycles, transitivity, SOCIAL NETWORKS, MODEL
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10046517
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