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National Academy of Sciences, Proceedings of the National Academy of Sciences, 23(105), p. 7907-7912, 2008

DOI: 10.1073/pnas.0707563105

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Optimal partition and effective dynamics of complex networks

Journal article published in 2008 by Weinan E. ORCID, Tiejun Li, Eric Vanden-Eijnden
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

Given a large and complex network, we would like to find the best partition of this network into a small number of clusters. This question has been addressed in many different ways. Here we propose a strategy along the lines of optimal prediction for the Markov chains associated with the dynamics on these networks. We develop the necessary ingredients for such an optimal partition strategy, and we compare our strategy with the previous ones. We show that when the Markov chain is lumpable, we recover the partition with respect to which the chain is lumpable. We also discuss the case of well-clustered networks. Finally, we illustrate our strategy on several examples.