Complex network zeta function: Difference between revisions

Revision as of 11:27, 26 June 2010

Revision as of 12:50, 23 October 2010

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Different definitions have been given for the dimension of a [[complex network]] or [[graph theory|graph]]. For example, [[Metric dimension (graph theory)| metric dimension]] is defined in terms of the resolving set for a graph. Dimension has also been [[Fractal dimension on networks|defined]] based on the [[Minkowski-Bouligand dimension|box covering method]] applied to graphs<ref name=goh>K.-I. Goh, G. Salvi, B. Kahng and D. Kim, Phys. Rev.

Lett. 96, 018701 (2006).</ref>. Here we describe the definition based on the '''complex network zeta function'''<ref name="Shankerb">{{cite journal|author=O. Shanker|year=2007|title=Graph Zeta Function and Dimension of Complex Network|journal=Modern Physics Letters B|volume= 21(11)|pages=639–644|doi=10.1142/S0217984907013146 | issue=11}}</ref>. This generalises the definition based on the scaling property of the volume with distance<ref name="Shankera">{{cite journal|author=O. Shanker|year=2007|title=Defining Dimension of a Complex Network |journal=Modern Physics Letters B|volume= 21(6)|pages=321–326|doi=10.1142/S0217984907012773 | issue=6}}</ref>. The best definition depends on the application.

==Definition==

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[[Category:Graph theory]]

[[Category:Dimension]]

[[Category:networkNetwork theory]]