Evolution of a large online social network

Although recently there are extensive research on the collaborative networks and online communities, there is very limited knowledge about the actual evolution of the online social networks (OSN). In the Letter, we study the structural evolution of a large online virtual community. We find that the scale growth of the OSN shows non-trivial S shape which may provide a proper exemplification for Bass diffusion model. We reveal that the evolutions of many network properties, such as density, clustering, heterogeneity and modularity, show non-monotone feature, and shrink phenomenon occurs for the path length and diameter of the network. Furthermore, the OSN underwent a transition from degree assortativity characteristic of collaborative networks to degree disassortativity characteristic of many OSNs. Our study has revealed the evolutionary pattern of interpersonal interactions in a specific population and provided a valuable platform for theoretical modeling and further analysis.

💡 Research Summary

This paper presents a longitudinal analysis of Wealink, a large professional‑oriented social networking site in China, using 27 monthly snapshots collected from May 2005 to August 2007. By treating users as nodes and friendship ties as undirected edges, the authors track the evolution of nine key network metrics: size (nodes and edges), density, average shortest‑path length, diameter, clustering coefficient, degree distribution, heterogeneity index, modularity, and degree assortativity.

The growth of nodes and edges follows a classic S‑shaped curve, which the authors fit with the Bass diffusion model’s logistic function, indicating that membership and link formation spread through the community much like an epidemic of adoption. Density exhibits a three‑stage pattern—initial rise, subsequent decline, and a gradual rebound—reflecting an early enthusiasm burst, a “dying‑out” phase, and eventual equilibrium.

Average path length and diameter first increase as density falls, then sharply shrink once new edges begin to connect previously distant parts of the network, a phenomenon also reported in Flickr, Yahoo! 360, and Internet AS‑level graphs. Clustering coefficients remain substantially higher than those of degree‑preserving randomized networks and correlate positively with density, underscoring the role of occupational and topic‑based “discussion groups” in fostering triadic closure.

Degree distribution evolves from an exponential‑like shape toward a power‑law with exponent γ≈1.74. The presence of groups limited to 30 members creates noticeable peaks at multiples of 30 in the distribution, highlighting the impact of platform‑imposed community structures on degree heterogeneity. The heterogeneity index H follows a non‑monotonic trajectory before stabilizing, confirming that the network settles into a steady heterogeneous state.

Modularity Q stays above 0.3 throughout, steadily increasing and eventually plateauing, indicating increasingly pronounced community structure driven by shared occupations and interests. Randomized counterparts show lower Q values, confirming that the observed modularity is not a trivial consequence of the degree sequence.

The most striking finding is the transition in degree assortativity. Early in the observation period, the Pearson correlation coefficient r is positive, reflecting assortative mixing typical of collaborative networks where high‑degree nodes tend to connect with each other. Around month 17, r flips to negative, indicating a shift to disassortative mixing where low‑degree users preferentially attach to high‑degree “elite” nodes. Randomized networks remain near zero throughout, demonstrating that this transition is driven by genuine structural dynamics rather than chance. The authors interpret the early assortativity as inheritance from offline social ties, while the later disassortativity reflects a virtual‑world tendency for newcomers to seek visibility by linking to well‑connected users.

Comparisons with other OSNs (e.g., MySpace, Facebook, Cyworld) show similar S‑shaped growth and shrinking diameters, but the assortativity‑to‑disassortativity transition appears novel. The study therefore contributes a comprehensive empirical portrait of how a large professional OSN matures: it grows according to diffusion dynamics, its density, clustering, heterogeneity, and modularity evolve non‑monotonically, its path length contracts, and its mixing pattern fundamentally changes over time. These insights challenge the assumption that social networks retain a fixed assortative or disassortative character and suggest that online platforms can undergo distinct structural phases driven by both offline social inheritance and online preferential attachment mechanisms.