Maximal dispersion of adaptive random walks (by G. Di Bona, L. Di Gaetano, V. Latora, and F. Coghi)

Implementation of adaptive random walk (ARW), unbiased random walk (URW), and maximum entropy random walk (MERW) on complex networks. In this folder you can find all the code, scripts and notebooks to run the simulations and analysis them as done in our paper.

Installation

1. Clone this directory to your computer in a new folder.

2. In order to ensure that everything is working as intended, create a dedicated environment using the specified requirements file, using:

   conda env create -f ARW.yml

   ACHTUNG: If you want to specify a specific install path rather than the default for your system, just use the -p flag followed by the required path, e.g.:

   conda env create -f ARW.yml -p /home/user/anaconda3/envs/ARW

How to use

In codes/functions.py there are all the basic functions needed to create or load graphs, and to run simulations.

Currently the only algorithms supported are URW, MERW and ARW. If for example you want to simulate an ARW, you need to do two things:

1. Load a graph, using the function load_graph with the parameters you want.
   • ACHTUNG: at the moment, the only graphs supported are Erdos-Renyi and Barabasi-Albert. If the requested graph is not already present in the folder, it is created from scratch, and its largest connected component is dumped and returned.
   • There is also support for an Airport network, i.e., a network between worldwide cities that have a direct flight, but you need to download the files from the owner of the dataset, i.e. from http://seeslab.info/downloads/air-transportation-networks/. Accessing this network from the file global-net.dat on 01/01/2022, it is made of 3618 nodes and 14142 links. If you use this network, remember to cite their work (see link). We suggest to put this file inside ./graphs/.
2. Run all_RW_preprocessing_entropy_theoretic with the parameters you want, specifying ARW as the algorithm.
   • ACHTUNG: the function all_RW_preprocessing_entropy_theoretic to run the process uses numba.njit, which speeds up the process. However, if you want to change the code under njit, beware that not all python functions are supported, and you need to be consistent with the types. See https://numba.pydata.org/numba-doc/latest/user/index.html.
   • Notice also that the function is slowed down (a lot) if you do prints under njit. Moreover, if you put a print inside a njit function, the print might appear in output after some time.

Scripts

There are some python scripts you can use to do all the simulations needed to make the plots in the paper. In particular, these are stored inside the folder ./codes/.

These codes need the proper arguments. If you have a cluster, you can use the ./bash_scripts/ files, in which all parameters and the correct codes are properly set. ACHTUNG: before running the bash script, enter inside the output subfolder and run the script from there. Notice indeed in these .sh scripts the change of folders.

If you are running the scripts in your local machine, you can use the same bash scripts for a guide to run all the necessary files in the correct way.

If you do not have enough computational resources, you can reduce the number of iterations for each set of parameters and algorithm, or you can change the size of the graphs and number of time steps. Moreover, you can create new scripts that use more than one core at a time, doing more simulations within the same process, by changing appropriately the parameters and, eventually, the code.

All created graphs are stored under ./graphs/, while all simulation results are stored in the proper subdirectories under ./data/, categorized depending on the parameters chosen and the type of simulation done.

You can also play more with the codes and create new sets of parameters to study new things.

Analysis

After all needed simulations are done, you can do the analysis and create the plots using ./notebooks/plots_analysis.ipynb. If you have done all simulations correctly, you should be able to run the whole notebook flawlessly, and the figures will be created under ./figures/.

Reference

If you use any of the material here provided, you must cite our work using the following bibtex entry:

@article{dibona2022maximal,
  title={Maximal dispersion of adaptive random walks},
  author={Di Bona, Gabriele and Di Gaetano, Leonardo and Latora, Vito and Coghi, Francesco},
  journal={Physical Review Research},
  volume={4},
  number={4},
  pages={L042051},
  year={2022},
  publisher={APS},
  doi={10.1103/PhysRevResearch.4.L042051}
}

Contact

If you need to contact us for any reason, please do not hesitate to send an email to francesco.coghi@su.se and, especially for code related reasons, to g.dibona@qmul.ac.uk.

Thank you for the interest and for using this repository,

The authors