A Geometric Preferential Attachment Model of Networks II
- Abraham D. FlaxmanAffiliated withDepartment of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213
- , Alan M. FriezeAffiliated withDepartment of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213
- , Juan VeraAffiliated withDepartment of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213
A detailed understanding of expansion in complex networks can greatly aid in the design and analysis of algorithms for a variety of important network tasks, including routing messages, ranking nodes, and compressing graphs. This has motivated several recent investigations of expansion properties in real-world graphs and also in random models of real-world graphs, like the preferential attachment graph. The results point to a gap between real-world observations and theoretical models. Some real-world graphs are expanders and others are not, but a graph generated by the preferential attachment model is an expander whp .
We study a random graph G n that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with power-law degree distribution where the expansion property depends on a tunable parameter of the model.
The vertices of G n are n sequentially generated points x 1,x 2,...,x n chosen uniformly at random from the unit sphere in . After generating x t , we randomly connect it to m points from those points in x 1,x 2,...,x t − 1 ....
- A Geometric Preferential Attachment Model of Networks II
- Book Title
- Algorithms and Models for the Web-Graph
- Book Subtitle
- 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings
- pp 41-55
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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