On the limit value of compactness of some graph classes

  • In this paper, we study the limit of compactness which is a graph index originally introduced for measuring structural characteristics of hypermedia. Applying compactness to large scale small-world graphs (Mehler, 2008) observed its limit behaviour to be equal 1. The striking question concerning this finding was whether this limit behaviour resulted from the specifics of small-world graphs or was simply an artefact. In this paper, we determine the necessary and sufficient conditions for any sequence of connected graphs resulting in a limit value of CB = 1 which can be generalized with some consideration for the case of disconnected graph classes (Theorem 3). This result can be applied to many well-known classes of connected graphs. Here, we illustrate it by considering four examples. In fact, our proof-theoretical approach allows for quickly obtaining the limit value of compactness for many graph classes sparing computational costs.

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Author:Tatiana Lokot, Alexander MehlerORCiDGND, Olga Abramov
Pubmed Id:https://pubmed.ncbi.nlm.nih.gov/30458027
Parent Title (English):PLoS one
Place of publication:Lawrence, Kan.
Contributor(s):Siamak Yassemi
Document Type:Article
Year of Completion:2018
Date of first Publication:2018/11/20
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2018/11/22
Tag:Geodesics; Graph theory; Hypertext; Sequence analysis
Issue:(11): e0207536
Page Number:8
First Page:1
Last Page:8
Copyright: © 2018 Lokot et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoCreative Commons - Namensnennung 4.0