Shortest-Path Percolation on Scale-Free Networks

This repository contains the code for

• Minsuk Kim, Lorenzo Cirigliano, Claudio Castellano, Hanlin Sun, Robert Jankowski, Anna Poggialini, and Filippo Radicchi, Shortest-Path Percolation on Scale-Free Networks, Physical Review E 113, 014314 (2026).

• Preprint (arXiv)

• BibTex entry:

  @article{kim2026shortest,
    title = {Shortest-path percolation on scale-free networks},
    author = {Kim, Minsuk and Cirigliano, Lorenzo and Castellano, Claudio and Sun, Hanlin and Jankowski, Robert and Poggialini, Anna and Radicchi, Filippo},
    journal = {Phys. Rev. E},
    volume = {113},
    issue = {1},
    pages = {014314},
    numpages = {9},
    year = {2026},
    month = {Jan},
    publisher = {American Physical Society},
    doi = {10.1103/pk8t-px35},
    url = {https://link.aps.org/doi/10.1103/pk8t-px35}
  }
  
  

How to Run the Code

We provide a makefile that compiles the source codes. You can compile it by typing:

make

Then, you can run the code as follows:

efficient_SPP_SFN.out <N> <lambda> <k_min> <C> <num_iter> <num_instance> <output_file_name>

where N is the size of the ER graph, lambda is the degree exponent, k_min is the minimum degree of the uncorrelated configuration model, C is the maximum shortest-path length, num_iter is the number of iterations of the shortest-path percolation on a single instance of the scale-free network, num_instance is the number of instances of the scale-free networks, and output_file_name is the name of the output file.

Due to the nature of the Newman-Ziff algorithm which saves the whole phase diagram of each realization, saving files for large-scale networks can consume a lot of space. Thus, we provide another code which only samples the observables when there is the largest drop in the size of the giant cluster, i.e., sampling observables under the event-based ensemble.

You can run the code as follows:

efficient_SPP_SFN_event.out <N> <lambda> <k_min> <C> <num_iter> <num_instance> <output_file_name>

where the arguments are same as mentioned above.