Welcome to the Documentation for NetworkFm!

NetworkFm is a Python package for the econometric analysis of the dyadic network formation models with degree heterogeneity.

This package accompanies the paper:

Yan, Zizhong; Li, Jingrong; Zhang, Yi (2026). Penalized Likelihood for Dyadic Network Formation Models with Degree Heterogeneity. arXiv e-prints, arXiv:2605.00771.

Project’s GitHub homepage: github.com/zizhongyan/networkfm

If you are new to the package, I recommend starting with Getting started, then working through the Examples section. The API reference section for detailed function/class documentation.

Table of Contents

• Getting Started
  • Prerequisites
  • Installation options
    • 1. Install from PyPI (recommended)
    • 2. Install the development version from GitHub
    • 3. Install from a local copy
  • Main entry: networkfm.fit()
    • Inputs: adjacency matrix G
    • Inputs: regressors X and Z
    • Model selection: directed and mutual
    • Bias correction method: bc_method
    • Estimation algorithm: algorithm
    • Separated nodes: drop_separation
    • Output control: silent
    • Average partial effects: ape
    • Tetrad/quadruple indices
    • Starting values: sv
    • Returned object and key attributes
  • Where to go next

• Examples Gallery
  • Data requirements used throughout this page
    • Data sources in the examples
  • Example 1: Trade network application (Helpman, Melitz and Rubinstein, 2008)
    • Data loading and preparation
    • Example 1.1: Dyadic network formation with both directed and mutual utilities
    • Example 1.2: Dyadic network formation with directed utility only
    • Example 1.3: Dyadic network formation with mutual utility only (undirected network)
  • Example 2: Conditonal-likelihood methods in networkfm
    • Artificial data for the examples
    • Example 2.1: Tetrad logit (undirected network)
    • Example 2.2: Quadruple logit (directed, no mutual utility)
    • Example 2.3: Speed-up via precomputing tetrad/quadruple indices
  • Where to go next

• API Reference
  • Data generation for examples and testing
    • networkfm.database.helpman09
    • networkfm.demo.GenData
    • networkfm.demo.NetworkGenDataMC
  • Tetrad/quadruple indices
    • networkfm.netrics.generate_tetrad_indices
    • networkfm.quadlogit.generate_quad_indices
  • Estimation interface
    • networkfm.fit

Code maintainer

Zizhong Yan, Institute for Economic and Social Research (IESR), Jinan University, Guangzhou, China. Email: helloyzz@gmail.com