Complex network zeta function

Different definitions have been given for the dimension of a complex network or graph. For example, metric dimension is defined in terms of the resolving set for a graph. Dimension has also been defined based on the box covering method applied to graphs.^[1] Here we describe the definition based on the complex network zeta function.^[2] This generalises the definition based on the scaling property of the volume with distance.^[3] The best definition depends on the application.

^ Goh, K.-I.; Salvi, G.; Kahng, B.; Kim, D. (2006-01-11). "Skeleton and Fractal Scaling in Complex Networks". Physical Review Letters. 96 (1). American Physical Society (APS): 018701. arXiv:cond-mat/0508332. doi:10.1103/physrevlett.96.018701. ISSN 0031-9007. PMID 16486532.
^ O. Shanker (2007). "Graph Zeta Function and Dimension of Complex Network". Modern Physics Letters B. 21 (11): 639–644. Bibcode:2007MPLB...21..639S. doi:10.1142/S0217984907013146.
^ O. Shanker (2007). "Defining Dimension of a Complex Network". Modern Physics Letters B. 21 (6): 321–326. Bibcode:2007MPLB...21..321S. doi:10.1142/S0217984907012773.

[goh-1] Goh, K.-I.; Salvi, G.; Kahng, B.; Kim, D. (2006-01-11). "Skeleton and Fractal Scaling in Complex Networks". Physical Review Letters. 96 (1). American Physical Society (APS): 018701. arXiv:cond-mat/0508332. doi:10.1103/physrevlett.96.018701. ISSN 0031-9007. PMID 16486532.

[Shankerb-2] O. Shanker (2007). "Graph Zeta Function and Dimension of Complex Network". Modern Physics Letters B. 21 (11): 639–644. Bibcode:2007MPLB...21..639S. doi:10.1142/S0217984907013146.

[Shankera-3] O. Shanker (2007). "Defining Dimension of a Complex Network". Modern Physics Letters B. 21 (6): 321–326. Bibcode:2007MPLB...21..321S. doi:10.1142/S0217984907012773.

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