On Power Law Growth of Social Networks

Abstract

What is the growth dynamics of social networks, like Facebook or WeChat? Does it truly exhibit exponential early-growth, as predicted by the celebrated models, like the Bass model? How about the dynamics of links, for which there are few published models? For the first time, we examine the growth of WeChat which is the largest online social network in China, together with several other real social networks. We observe Power-Law growth dynamics for both nodes and links, a fact that breaks the textbook models featuring Sigmoid curves. We propose NetTide , along with differential equations for the growth of nodes and links. Our model fits the growth dynamics of real social networks well; it encompasses many traditional growth dynamics as special cases, while remaining parsimonious in parameters. The NetTide for link growth is the first one of its kind, accurately fitting real data, and capturing densification phenomenon. We further formulate two stochastic generators, which interpret the growth of nodes and links through survival analysis and micro-level interactions within a social network, respectively. The proposed generators reproduce realistic growth dynamics of social networks. When applied on the WeChat data, our NetTide forecasted $\geq$ 730 days ahead with 3 percent error.