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Seeded PageRank solution paths

Published online by Cambridge University Press:  01 July 2016

D. F. GLEICH  and
K. KLOSTER
D. F. GLEICH
Affiliation:
Department of Computer Science, Purdue University, West Lafayette IN, USA email: dgleich@purdue.edu
K. KLOSTER
Affiliation:
Department of Mathematics, Purdue University, West Lafayette IN, USA email: kkloste@purdue.edu
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Abstract

We study the behaviour of network diffusions based on the PageRank random walk from a set of seed nodes. These diffusions are known to reveal small, localized clusters (or communities), and also large macro-scale clusters by varying a parameter that has a dual-interpretation as an accuracy bound and as a regularization level. We propose a new method that quickly approximates the result of the diffusion for all values of this parameter. Our method efficiently generates an approximate solution path or regularization path associated with a PageRank diffusion, and it reveals cluster structures at multiple size-scales between small and large. We formally prove a runtime bound on this method that is independent of the size of the network, and we investigate multiple optimizations to our method that can be more practical in some settings. We demonstrate that these methods identify refined clustering structure on a number of real-world networks with up to 2 billion edges.

Keywords

Random walks on graphsgraphs and linear algebra (matrices, eigenvalues, etc.)programming involving graphs or networkssocial networkscomplex networks
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Special Issue 6: Network Analysis and Modelling , December 2016 , pp. 812 - 845
Copyright
Copyright © Cambridge University Press 2016 

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