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Structural complexity of one-dimensional random geometric graphs

Abstract:

We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by n nodes randomly scattered in [0, 1] that connect if they are within the connection range r∈[0,1] . We provide bounds on the number of possible structures which give universal upper bounds on the structural entropy that hold for any n , r and distribution of the node locations. For fixed r , the number of structures is Θ(a2n) with a=a(r)=2cos(π⌈...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1109/TIT.2022.3207819

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Engineering Science
Role:
Author
ORCID:
0000-0003-1581-5598
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Name:
Engineering and Physical Sciences Research Council
Grant:
EP/T02612X/1
Publisher:
Institute of Electrical and Electronics Engineers
Journal:
IEEE Transactions on Information Theory More from this journal
Volume:
69
Issue:
2
Pages:
794-812
Publication date:
2022-09-19
Acceptance date:
2022-09-08
DOI:
ISSN:
0018-9448
Language:
English
Keywords:
Pubs id:
1279019
Local pid:
pubs:1279019
Deposit date:
2022-09-16

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