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A generalized Louvain method for community detection implemented in MATLAB spread retract

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## GenLouvain Version 2.2

### released July 2019

Please cite this code as Lucas G. S. Jeub, Marya Bazzi, Inderjit S. Jutla, and Peter J. Mucha,
"A generalized Louvain method for community detection implemented in MATLAB," https://github.com/GenLouvain/GenLouvain (2011-2019).

## Contents:

This package consists of the main genlouvain.m file which calls a number of subroutines implemented as mex functions. Source code for the mex files is included in the "MEX_SRC" directory. Pre-compiled executables for 64bit Mac, Windows, and Linux systems are included in the private directory. It also includes iterated_genlouvain.m which iteratively applies genlouvain on the output partition of the previous run with optional post-processing. Functions to compute modularity matrices and to post-process partitions are included in the "HelperFunctions" directory. The post-processing functions solve optimal assignment problems using code by Markus Buehren (included in the "Assignment" directory and available at https://uk.mathworks.com/matlabcentral/fileexchange/6543-functions-for-the-rectangular-assignment-problem/content/assignmentoptimal.m).

## Installation instructions:

Make sure that the "GenLouvain" folder and all its subfolders are on the MATLAB path to ensure that all dependencies between functions are accessible.

If the mex executables for your system are not in the private directory, you will need to compile these files on your system by running the compile_mex.m script from the "MEX_SRC" directory (check the mex documentation in your MATLAB). If you would like to share these compiled files with other users, email them to Peter Mucha (mucha@unc.edu).

## Changes from previous versions:

#### Support for multiple aspects

Version 2.2 of GenLouvain adds support for multilayer networks with multiple aspects (see "multiaspect.m" in "HelperFunctions").

Version 2.1 of GenLouvain also a implements a new 'moverandw' option which chooses moves at random with a probability proportional to the increase in the quality function. This is in addition to the 'moverand' option from Version 2.0 which chooses moves uniformly at random from all possible moves that improve the quality function.

#### Increased speed:

Version 2.1 removes quadratic bottlenecks that could become noticeable for very large networks (millions of nodes). The mex functions have also been optimized further.

#### Generate modularity matrices:

Version 2.1 includes a folder "HelperFunctions" with functions to generate different types of monolayer and multilayer modularity matrices.

#### Iterated GenLouvain with postprocessing:

Includes iterated_genlouvain which iteratively restarts genlouvain with the output partition of the previous run (with optional post-processing). Post-processing functions for ordered and unordered multilayer partitions that increase the value of the quality function without changing partitions on each layer are included in "HelperFunctions". "HelperFunctions" also includes functions that compute "persistence" for ordered and unordered multilayer networks.

## Usage:

1. generate a modularity matrix for your network (see doc('HelperFunctions'))

2. use genlouvain or iterated_genlouvain to obtain a partition that approximately optimizes the corresponding modularity-like quality function

3. ideally repeat step 2 multiple times to check that the output is consistent between randomizations

The genlouvain.m function uses different methods for computing the change in modularity, depending on whether the modularity matrix is provided as a sparse matrix or not. Depending on the amount of sparsity in the modularity matrix, it may be faster to convert it to a full matrix.

More extensive documentation and example use of this code is provided online (http://netwiki.amath.unc.edu/GenLouvain) and in the individual functions (e.g., see doc('genlouvain') and doc('iterated_genlouvain')).

IMPORTANT NOTE: When using the multilayer quality function in Mucha et al. 2010, we recommend using iterated_genlouvain with 'moverandw' and the appropriate post-processing function (i.e., postprocess_ordinal_multilayer for an ordered multilayer network and postprocess_categorical_multilayer for an unordered multilayer network) for better results.

## Acknowledgments:

A special thank you to Stephen Reid, whose greedy.m code was the original version that has over time developed into the present code.

Thank you also to Dani Bassett, Jesse Blocher, Mason Porter and Simi Wang for inspiring improvements to the code.

## References:

Mucha, P. J., Richardson, T., Macon, K., Porter, M. A. & Onnela, J.-P. Community structure in time-dependent, multiscale, and multiplex networks. Science 328, 876-878 (2010).

The codes included in this directory are provided for broad use under a minor (last line) modification of the "FreeBSD License" (see License.txt)

Notes on OCTAVE compatibility:

The compile_mex.m script from the MEX_SRC directory creates OCTAVE .mex files when run from OCTAVE.

If you are trying to use this from the old 3.4.0 .app bundle version of OCTAVE for Mac, you will need to fix OCTAVE's build configuration first (or you may want to consider upgrading to a recent 3.8.x version where this seems to work out of the box):

1. Ensure that the environment variables CXX and DL_LD point to a C++ compiler installed on your system (e.g. by running setenv(‘CXX’,’/usr/bin/g++’) setenv(‘DL_LD’,’/usr/bin/g++’) where ‘/usr/bin/g++’ may need to be replaced with the path to your compiler depending on your system configuration).

2. Include the ‘-arch i386’ option in CXXFLAGS and LDFLAGS by running setenv('CXXFLAGS',[getenv('CXXFLAGS'),' -arch i386']) setenv('LDFLAGS',[getenv('LDFLAGS'),' -arch i386']) to create 32bit binaries.

3. Change line 52 of /Applications/Octave.app/Contents/Resources/include/octave-3.4.0/octave/mexproto.h from #include <cstdlib> to #include <stdlib.h> to avoid a conflict from including two different versions of the standard library.

4. Finally run compile_mex to compile the binaries.