HyperSIS

Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks

Code implemented using the Fortran Package Manager.

Main paper: Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks, by Hugo P. Maia, Wesley Cota, Yamir Moreno, and Silvio C. Ferreira.

Reference: arxiv:2509.20174 DOI:10.48550/arXiv.2509.20174

Hyper-SIS Dynamical Model

This code simulates SIS dynamics on hypergraphs (Hyper-SIS). Each of the $N$ agents can be either susceptible ($\sigma_i = 0$) or infected ($\sigma_i = 1$). Infections occur via hyperedges, which are active if a critical mass of members is infected, while infected nodes recover spontaneously.

Key points:

• Node recovery rate: $\alpha = 1$.
• Hyperedge activation threshold: $\theta(m) = 1 + (m-1)\theta_0$, where $m$ is the hyperedge order.
• Infection rate as a function of hyperedge order: $\beta(m) = \beta[1 + b(m-1)]$.
• Pairwise infection rate: $\beta(1) = \beta$.
• Parameters par_b and par_theta correspond to $b$ and $\theta_0$.

See the main paper for full details.

Using it as a dependency

Add this package as a dependency using the Fortran Package Manager (fpm):

[dependencies]
hyperSIS.git = "https://github.com/gisc-ufv/hyperSIS"

See the documentation and main program for details.

Python package Installation

The easiest way to use this project is through its Python interface.

This package will be published on PyPI in the future. Until then, you need to clone the repository manually.

Before installing, make sure that at least one Fortran compiler is available. By default, the package assumes GNU Fortran (gfortran) installed and available in your PATH. See Installing GFortran for help.

Steps:

1. Clone the repository:

   sh git clone https://github.com/gisc-ufv/hyperSIS.git cd hyperSIS

2. Activate your preferred Python environment (e.g., venv, conda, etc.):

   ```sh

   Example with venv

   python -m venv venv source venv/bin/activate

   Example with conda

   conda create -n hyperSIS python=3.11 conda activate hyperSIS ```

3. Install the Python package:

   sh pip install ./python

4. Verify if gfortran and fpm are accessible:

   sh gfortran --version fpm --version

5. (Optional) A Google Colab notebook demonstrating all installation and usage steps is available here.

Usage

See examples.ipynb for examples.

Import the package with

import hyperSIS as hs

The simulation interface revolves around two main objects:

1. SimulationArgs A dataclass containing all parameters required to configure a hyperSIS simulation, including network specification, algorithm choices, temporal settings, initial conditions, and epidemic parameters.

2. run_simulation(beta1: float, args: SimulationArgs) The function that executes the simulation with the given arguments. Returns a SimulationResult object containing the processed results, including network mapping, temporal evolution, and statistics of infected nodes.

Simulation arguments

The SimulationArgs dataclass contains all configurable parameters for running a hyperSIS simulation.

• verbose: bool Enable verbose output. Default: True

• verbose_level: str Logging level: 'info', 'warning', 'error', 'debug'. Default: warning

• seed: int Random seed for reproducibility. Default: 42

• remove_files: bool Remove temporary files after execution. Default: False

• network: NetworkFormat Network specification as a tuple. Optional parameters are in brackets:

• ("edgelist", path, [delimiter], [comment], [cache])
• ("fortran-edgelist", path, [cache])
• ("bipartite", path, [delimiter], [comment], [cache])
• ("xgi", name_or_object, [cache])
• ("xgi_json", path, [cache])
• ("hif", path, [cache])

• ("PL", gamma, N, [sample]) Default: ("edgelist", "example.edgelist", None, "#", False)

• output_dir: Optional[str] Directory to store simulation output. If None, a temporary folder is used. Default: None

• algorithm: str Simulation algorithm: 'HB_OGA' or 'NB_OGA'. Default: HB_OGA

• sampler: str Sampling method: 'rejection_maxheap' or 'btree'. Default: btree

• tmax: int Maximum simulation time. Default: 100

• use_qs: bool Whether to use the quasi-stationary method. Default: False

• n_samples: int Number of samples per simulation. Default: 10

• time_scale: str Temporal scale for output: 'uniform' or 'powerlaw'. Default: uniform

• initial_condition: tuple Initial state specification:

• ('fraction', float) → fraction of infected nodes

• ('number', int) → exact number of initially infected nodes Default: ("fraction", 1.0)

• export_states: bool Whether to export the full state trajectory. Default: False

• par_b: float Epidemic infection rate scale $b$ in $\beta(m) = \beta[1 + b(m-1)]$. Default: 0.5

• par_theta: float Epidemic critical mass threshold $\theta_0$ in $\theta(m) = 1 + (m-1)\theta_0$. Default: 0.5

Function

run_simulation(beta1: float, args: SimulationArgs)

Runs a Hyper-SIS simulation on the specified network.

Parameters:

• beta1: float Base infection rate $\beta(1)$ for pairwise interactions.
• args: SimulationArgs Simulation parameters, including network specification, algorithm choice, number of samples, initial condition, and epidemic parameters par_b and par_theta.

Returns:

• SimulationResult Object containing:

• network: NetworkFormat – the network specification used.

• node_map: dict – mapping from original node IDs to Fortran node IDs.
• temporal: TemporalResult – temporal dynamics with:
  • t: np.ndarray – mean time per Gillespie tick.
  • rho_avg: np.ndarray – mean number of infected nodes over all runs.
  • rho_var: np.ndarray – variance of infected nodes.
  • n_samples: int – number of runs where infection is non-zero.

How to Cite

When using this package, please cite the following paper:

Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks, by Hugo P. Maia, Wesley Cota, Yamir Moreno, and Silvio C. Ferreira (2025)

Reference: arxiv:2509.20174 DOI:10.48550/arXiv.2509.20174

The BibTeX entry is:

@misc{maia2025hoga,
      title={Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks},
      author={Hugo P. Maia and Wesley Cota and Yamir Moreno and Silvio C. Ferreira},
      year={2025},
      eprint={2509.20174},
      archivePrefix={arXiv},
      primaryClass={physics.soc-ph},
      url={https://arxiv.org/abs/2509.20174},
}