From Small World Phenomenon to Correlation Analysis in a Temporal Landline Phone Call Network Graph Series

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 -worldness? 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 smallworld -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.