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Densification arising from sampling fixed graphs

Content Provider	ACM Digital Library
Author	Pedarsani, Pedram Figueiredo, Daniel R. Grossglauser, Matthias
Abstract	During the past decade, a number of different studies have identified several peculiar properties of networks that arise from a diverse universe, ranging from social to computer networks. A recently observed feature is known as network densification, which occurs when the number of edges grows much faster than the number of nodes, as the network evolves over time. This surprising phenomenon has been empirically validated in a variety of networks that emerge in the real world and mathematical models have been recently proposed to explain it. Leveraging on how real data is usually gathered and used, we propose a new model called Edge Sampling to explain how densification can arise. Our model is innovative, as we consider a fixed underlying graph and a process that discovers this graph by probabilistically sampling its edges. We show that this model possesses several interesting features, in particular, that edges and nodes discovered can exhibit densification. Moreover, when the node degree of the fixed underlying graph follows a heavy-tailed distribution, we show that the Edge Sampling model can yield power law densification, establishing an approximate relationship between the degree exponent and the densification exponent. The theoretical findings are supported by numerical evaluations of the model. Finally, we apply our model to real network data to evaluate its performance on capturing the previously observed densification. Our results indicate that edge sampling is indeed a plausible alternative explanation for the densification phenomenon that has been recently observed.
Starting Page	205
Ending Page	216
Page Count	12
File Format	PDF
ISBN	9781605580050
DOI	10.1145/1375457.1375481
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-06-02
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Densification Network modeling Edge sampling
Content Type	Text
Resource Type	Article

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