Self-Similarity in Social Network Dynamics

Abstract

Analyzing and modeling social network dynamics are key to accurately predicting resource needs and system behavior in online social networks. The presence of statistical scaling properties, that is, self-similarity, is critical for determining how to model network dynamics. In this work, we study the role that self-similarity scaling plays in a social network edge creation (that is, links created between users) process, through analysis of two detailed, time-stamped traces, a 199 million edge trace over 2 years in the Renren social network, and 876K interactions in a 4-year trace of Facebook. Using wavelet-based analysis, we find that the edge creation process in both networks is consistent with self-similarity scaling, once we account for periodic user activity that makes edge creation process non-stationary. Using these findings, we build a complete model of social network dynamics that combines temporal and spatial components. Specifically, the temporal behavior of our model reflects self-similar scaling properties, and accounts for certain deterministic non-stationary features. The spatial side accounts for observed long-term graph properties, such as graph distance shrinkage and local declustering. We validate our model against network dynamics in Renren and Facebook datasets, and show that it succeeds in producing desired properties in both temporal patterns and graph structural features.