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摘要
We study Facebook networks at 40 American universities, with focus on the comparison of their degree distributions and mechanism governing their evolution. We find that the heterogeneity indexes of these networks are all small compared with scale-free networks, and different from real-world social networks 5 Facebook networks show significant degree disassortativity; the exponent gamma for the power-law model of the degree distributions is large for the networks, indicating obvious homogeneity of network structure. We calculate the goodness-of-fit between the data and power law and find that the p-values are larger than threshold 0.1 for 20 networks, implying that power law is a plausible hypothesis; we compare the power-law model with 4 alternative competing distributions and find that power-law model gives the best fit for all 40 networks. However in wider interval of degrees some other distributions, such as log-normal or stretched exponential, can give the best fit. Further based on the homogeneity of Facebook we propose an analyzable model that integrates the introduction of new vertices and edges. The edges can be established either between new vertices and old vertices or between old vertices. The model captures the real evolution processes of Facebook networks and can well reproduce their degree distributions.
