Optimal partition and effective dynamics of complex networks

Weinan E, Tiejun Li, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)7907-7912
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number23
StatePublished - Jun 10 2008

All Science Journal Classification (ASJC) codes

  • General


  • Lumpability
  • MNCut
  • Partitioning
  • k means


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