We present a deterministic model for online social networks OSNs based on transitivity and local knowledge in social interactions. The ILT model provably satisfies a number of both local and global properties that have been observed in OSNs and other real-world complex networks, such as a densification power law, decreasing average distance, and higher clustering than in random graphs with the same average degree. Experimental studies of social networks demonstrate poor expansion properties as a consequence of the existence of communities with low numbers of intercommunity edges.
Bounds on the spectral gap for both the adjacency and normalized Laplacian matrices are proved for graphs arising from the ILT model indicating such bad expansion properties. A randomized version of the ILT model is presented that exhibits a tunable densification power-law exponent and maintains several properties of the deterministic model.
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Bonato , Hadi , Horn , Prałat , Wang : Models of Online Social Networks
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