Social graphs - change of metrics' distribution with scale

Social networks are systems that are generally composed of multiple entities interacting with each other to provide a desired functionality. The interactions between these entities can be modeled as graphs. Presenting these interactions in terms of graph models allows system designers to not only investigate and reason about their systems but also to design new solutions and applications. Real interaction data is required to build graph models. However, in many scenarios it is difficult to obtain real data because of restrictions, such as privacy issues, scale of the system and administrative restrictions. There has been done a great amount of work in the social graph crawling and modeling field, however there has not yet been conducted a study of how different metrics behave when the graph size is changing, combining observations from both modeling and sampling. Our contribution with this work is mapping how degree, clustering coefficient, closeness and betweenness distributions are affected by scale both for Watts-Strogatz models and when sampling with Random Walk, Breadth First Search and Metropolis-Hasting Random Walk. We argue that clustering coefficient distribution gets further away from the original values for smaller graphs, and that the rest of the metrics are not affected by scale. We also show that joint degree distribution metric is not under control of Watts-Strogatz model