Walk based Laplacians for Modeling Diffusion on Complex Networks

This repository contains the accompanying code for the article "Walk based Laplacians for Modeling Diffusion on Complex Networks".

You can clone the main repository and initialize all submodules at once with this command:

git clone --recurse-submodules https://github.com/Cirdans-Home/walk-laplacian.git

the --recurse-submodules tells Git to automatically initialize and update each submodule.

Tip

If you’ve already cloned the repository without initializing submodules, you can initialize and update them afterward:

git submodule update --init --recursive

Collaborators

• Francesca Arrigo 📧
• Fabio Durastante 📧 🔗

External codes

The code in this repository makes use of a number of external codes. In particular, it contains as Git submodules the 🔗 PSCToolkit library which is needed to repeat some of the experiments involving the solution of linear systems related to the Katz centrality-based Laplacian. Information about configuration and installation can be found in the READMEs contained in the 📂 configure and 📂 install folders.

The other needed codes are the Rational-Krylov Toolbox RKToolbox that can be obtained and installed by executing in the MATLAB shell the command:

unzip('http://guettel.com/rktoolbox/rktoolbox.zip'); 
cd('rktoolbox'); addpath(fullfile(cd)); savepath

and the 🔗 Algorithm 919. The get919.sh scripts downloads it and put it into the matlabsrc folder. If you are not running under Linux, you can download the zip file from the supplementary materials of the paper at the previous link.

Important

If you use the code contained in this repository and, in particular, the features inherited from external codes, please cite also the reference works for them.

@article{PSCToolkit,
title = {Parallel Sparse Computation Toolkit},
journal = {Software Impacts},
volume = {15},
pages = {100463},
year = {2023},
issn = {2665-9638},
doi = {https://doi.org/10.1016/j.simpa.2022.100463},
url = {https://www.sciencedirect.com/science/article/pii/S2665963822001476},
author = {Pasqua D’Ambra and Fabio Durastante and Salvatore Filippone},
keywords = {Linear solvers, Algebraic preconditioners, HPC, GPU, Heterogeneous computing},
}
@techreport{RKToolbox,
 title={A rational Krylov toolbox for MATLAB},
 author={Berljafa, Mario and Elsworth, Steven and G{\"u}ttel, Stefan},
 year={2014},
 institution={Manchester Institute for Mathematical Sciences, University of Manchester},
 url={http://guettel.com/rktoolbox/index.html},
}
@article{10.1145/2168773.2168781,
author = {Niesen, Jitse and Wright, Will M.},
title = {Algorithm 919: A Krylov Subspace Algorithm for Evaluating the ϕ-Functions Appearing in Exponential Integrators},
year = {2012},
issue_date = {April 2012},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {38},
number = {3},
issn = {0098-3500},
url = {https://doi.org/10.1145/2168773.2168781},
doi = {10.1145/2168773.2168781},
journal = {ACM Trans. Math. Softw.},
month = apr,
articleno = {22},
numpages = {19},
keywords = {Krylov subspace methods, exponential integrators, matrix exponential}
}

Running the experiments

The code to run the experiments is contained in the 📂 matlabsrc folder. The folder also contains the various routines that implement the walk-based Laplacians. See the README inside the folder for more information.