the components of a weighted graph by Markov clustering, MCL; MATLAB’s mclComponents

Syntax

A = mclComponents(job.graph, 1.6)

Until the columns settle.

A = mclComponents(job.graph, 1.6, maxIter=4)

At most four iterations.

Description

The steps of S. van Dongen’s algorithm repeated until the columns settle: the expansion A @ A, the inflation of every entry to the power p, the entries up to 1e-4 pruned and the columns normalised. Before, the entries up to 1e-4 are pruned, a graph with no symmetric entry made symmetric and, where the diagonal is empty, ones put on it. The larger p, the smaller the clusters; the nonzero pattern of the result joins the nodes of one cluster.

Input

`A`	sparse adjacency matrix, the weights between 0 and 1
`p`	the inflation power

Keywords

keyword	default	description
`maxIter`	`inf`	the iteration bound; the loop stops after maxIter - 1 steps

Output

`A`	sparse matrix of the clusters

References

S. van Dongen, Graph clustering by flow simulation, PhD thesis, University of Utrecht (2000)

Used on

MaParentGrainReconstructionAdvanced

MATLAB’s mclComponents

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/mclComponents_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

mclComponents