Conductance and congestion in power law graphs
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
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Theoretical Computer Science
Analysis of topological characteristics of huge online social networking services
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Measurement and analysis of online social networks
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Feedback effects between similarity and social influence in online communities
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A Course on the Web Graph
Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
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We present a deterministic model for on-line social networks based on transitivity and local knowledge in social interactions. In the Iterated Local Transitivity (ILT) model, at each time-step and for every existing node x , a new node appears which joins to the closed neighbour set of x . The ILT model provably satisfies a number of both local and global properties that were observed in real-world on-line social and other 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 number of inter-community links. A spectral gap for both the adjacency and normalized Laplacian matrices is proved for graphs arising from the ILT model, thereby simulating such bad expansion properties.