On the Distances that Friendship Ignores

Abstract

This article uses data from the project “The virtual population of Russia” to investigate the intensity of friendship between users of the social network site VKontakte living in different regions. This intensity can be seen as a measure of interregional interaction and of the proximity of extra-territorial regions. Quantitative friendship intensity between pairs of regions was measured as the ratio of total interregional friendship connections registered in VKontakte to the number of potentially possible friendship connections: the product of numbers of users in a pair of regions. We consider the dependence of friendship intensity on interregional distance under the assumption of an exponential decay of intensity as distance (measured between centers of regions as the crow flies regardless of the transport network) grows. The analysis of our data, namely the correlation between real friendship intensity and the modeled intensity computed as a function of distance, shows two different types of dependency between friendship intensity and distance: up to a certain threshold (approximately 500km), friendship intensity decreases as the distance grows, while at distances above this threshold the intensity of friendship demonstrates essentially no dependence on interregional distance. This threshold character of dependence is visible in both the entire data set and its parts, as long as they contain regions that are sufficiently far apart. The same value of the threshold follows from estimating the friendship intensity decay model parameters using a piecewise linear regression model.