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.
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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 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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