Abstract—Is a temporal landline phone call network graph series led by the presence of small world phenomenon? Are order and average vertex degree of the network graphs associated to small – world – ness? How are related size and order of the network graphs in this temporal series? A continuously graded notion of small – world – ness is used to study the presence of small world phenomenon. Spearman’s and Kendall’s correlation coefficients are used to perform a non – parametric correlation analysis between small – world – ness and order/average vertex degree. Linear regression on log – transformed quantities is used to analyse the relationship between size and order. It is achieved by the study that, the presence of small – world – ness is confirmed in each time step of the series, and there is no significant association between small – world – ness and graph order/average vertex degree. A significant positive power relationship between size and order is found.

Index Terms—Non–parametric correlation, small world, temporal network graph series.

The authors are with Department of Mathematics, University “Ismail Qemali”, Str. Kosova, 9400 Vlore, Albania (email: o.gjermeni@gmail.com).

Cite: Orgeta Gjermëni, Miftar Ramosaço, "From Small World Phenomenon to Correlation Analysis in a Temporal Landline Phone Call Network Graph Series," International Journal of Applied Physics and Mathematics vol. 7, no. 4, pp. 275-283, 2017.