Dimension theory of graphs and networks

Nowotny, Thomas and Requardt, Manfred (1998) Dimension theory of graphs and networks. Journal of Physics A, 31. pp. 2447-2463.

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Starting 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.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Informatics
Depositing User: Thomas Nowotny
Date Deposited: 06 Feb 2012 19:50
Last Modified: 22 Oct 2019 09:18
URI: http://sro.sussex.ac.uk/id/eprint/22456
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