The small-world phenomenon: an algorithmic perspective
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Graphs over time: densification laws, shrinking diameters and possible explanations
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Structure and evolution of online social networks
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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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Why we twitter: understanding microblogging usage and communities
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Protean graphs with a variety of ranking schemes
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Estimating node similarity from co-citation in a spatial graph model
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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
A geometric model for on-line social networks
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Assessing the effects of a soft cut-off in the twitter social network
NETWORKING'11 Proceedings of the 10th international IFIP TC 6 conference on Networking - Volume Part II
Modeling social networks through user background and behavior
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Effects of a soft cut-off on node-degree in the Twitter social network
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Innocent by association: early recognition of legitimate users
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SocialWatch: detection of online service abuse via large-scale social graphs
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
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We study the link structure of on-line social networks (OSNs), and introduce a new model for such networks which may help infer their hidden underlying reality. In the geo-protean (GEO-P) model for OSNs nodes are identified with points in Euclidean space, and edges are stochastically generated by a mixture of the relative distance of nodes and a ranking function. With high probability, the GEO-P model generates graphs satisfying many observed properties of OSNs, such as power law degree distributions, the small world property, densification power law, and bad spectral expansion. We introduce the dimension of an OSN based on our model, and examine this new parameter using actual OSN data. We discuss how the dimension parameter of an OSN may eventually be used as a tool to group users with similar attributes using only the link structure of the network.