Small world topologies of Facebook pages in Bahía Blanca

Abstract

Networks that exhibit large hubs are prone to show higher connectivity than random structures. This feature is also reflected in the presence of power law distribution in the degree distribution of nodes. We check for the presence of power law degree distributions in Facebook Page Networks (FPN). We analyze data collected from 325 Facebook fan pages from an Argentinian median city summarizing 94 thousand nodes and 6.5 million edges during a whole year. We found that whole network exhibits power law degree distributions but when we analyzed the subnetworks that compose it only a handful of marginal networks in terms of size and level of engagement. We find that main subnetworks exhibit small world properties such as average geodesic distance approximates and correlates to the natural logarithm of the graph range. We begin our contribution by surveying the topic of power law in degree distribution and small world in online networks. We estimate the slopes of the log-log degree distribution for each network for identifying free scale structures and statistically associate network structural properties with the presence of power law distributions. We present statistical results that associate structural parameters with the presence of power law distributions and small world effect shading light to new patterns for detecting the properties in networks.