File(s) not publicly available
Dimension theory of graphs and networks
journal contribution
posted on 2023-06-08, 00:12 authored by Thomas NowotnyThomas Nowotny, Manfred RequardtStarting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of continuum physics and mathematics. A core concept is the notion of dimension. In the following we develop such a notion for irregular structures such as (large) graphs and networks and derive a number of its properties. Among other things we show its stability under a wide class of perturbations which is important if one has ` dimensional phase transitions' in mind. Furthermore we systematically construct graphs with almost arbitrary ` fractal dimension' which may be of some use in the context of ` dimensional renormalization' or statistical mechanics on irregular sets.
History
Publication status
- Published
Journal
Journal of Physics AExternal DOI
Volume
31Page range
2447-2463Department affiliated with
- Informatics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC