## A Stochastic Uncoupling Process for Graphs (2000)

Venue: | NATIONAL RESEARCH INSTITUTE FOR MATHEMATICS AND COMPUTER SCIENCE IN THE |

Citations: | 2 - 1 self |

### BibTeX

@TECHREPORT{Dongen00astochastic,

author = {Stijn Van Dongen},

title = {A Stochastic Uncoupling Process for Graphs},

institution = {NATIONAL RESEARCH INSTITUTE FOR MATHEMATICS AND COMPUTER SCIENCE IN THE},

year = {2000}

}

### OpenURL

### Abstract

A discrete stochastic uncoupling process for finite spaces is introduced, called the Markov Cluster Process. The process takes a stochastic matrix as input, and then alternates flow expansion and flow inflation, each step defining a stochastic matrix in terms of the previous one. Flow expansion corresponds with taking the k th power of a stochastic matrix, where k 2 IN . Flow inflation corresponds with a parametrized operator \Gamma r , r 0, which maps the set of (column) stochastic matrices onto itself. The image \Gamma r M is obtained by raising each entry in M to the r th power and rescaling each column to have sum 1 again. In practice the process converges very fast towards a limit which is idempotent under both matrix multiplication and inflation, with quadratic convergence around the limit points. The limit is in general extremely sparse and the number of components of its associated graph may be larger than the number associated with the input matrix. This uncoupli...