Complex network zeta function: Difference between revisions

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

==Definition==