Revision as of 04:11, 31 May 2010 edit Oshanker (talk \| contribs) 82 edits →Definition: Described the new concept - using supremum to avoid the need for averaging over nodes. ← Previous edit		Revision as of 04:13, 31 May 2010 edit undo Oshanker (talk \| contribs) 82 edits m doi information Next edit →
Line 14: :<math> \langle k \rangle = \lim_{\alpha \rightarrow \infty} \zeta_G ( \alpha ). </math> The need for taking an average over all nodes can be avoided by using the concept of supremum over nodes, which makes the concept much easier to apply for formally infinite graphs<ref name="ShankerTCS">{{cite journal\|author=O. Shanker\|year=2010\|title=Complex Network Dimension and Path Counts\|journal=Theoretical Computer Science\|volume= 411\|pages=2454–2458\|doi:10.1016/j.tcs.2010.02.013 }}</ref>.The definition can be expressed as a weighted sum over the node distances. This gives the Dirichlet series relation :<math> \zeta_G ( \alpha ) = \sum_{r}S(r)/r^{\alpha}. </math>

Complex network zeta function: Difference between revisions