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NEMtropy is a Maximum-Entropy toolbox for networks, it provides the user with a state of the art solver for a range variety of Maximum Entropy Networks models derived from the ERGM family. This module allows you to solve the desired model and generate a number of randomized graphs from the original one: the so-called graphs ensemble.

Project description

PyPI PyPI - Python Version License: GPL v3 ArXiv

NEMtropy: Network Entropy Maximization, a Toolbox Running On PYthon

NEMtropy is a Maximum-Entropy toolbox for networks, released as a python3 module.

NEMtropy provides the user with a state of the art solver for a range variety of Maximum Entropy Networks models derived from the ERGM family. This module allows you to solve the desired model and generate a number of randomized graphs from the original one: the so-called graphs ensemble.

NEMtropy builds on the current literature on the matter, improving both in speed of convergence and in the scale of the feasible networks. To explore Maximum-Entropy modeling on networks, checkout Maximum Entropy Hub.

The models implemented in NEMtropy are presented in a forthcoming paper on arXiv. If you use the module for your scientific research, please consider citing us:

          title={Fast and scalable likelihood maximization for Exponential Random Graph Models}, 
          author={Nicolò Vallarano and Matteo Bruno and Emiliano Marchese and Giuseppe Trapani and Fabio Saracco and Tiziano Squartini and Giulio Cimini and Mario Zanon},

Table Of Contents

Currently Implemented Models

The main feature of NEMtropy is (but not limited to) network randomization. The specific kind of network to randomize and property to preserve defines the model you need:

  • UBCM Undirected Binary Configuration Model [1]
  • UECM Undirected Enhanced Configuration Model [1]
  • DBCM Directed Binary Configuration Model [1]
  • DECM Directed Enhanced Configuration Model [1]
  • CReMa [2]
  • BiCM Bipartite Configuration Model [3]

The following table may helps you identify the model that fits your needs in function of the type of network you are working with; for in-depth discussion please see the references.

[...] Undirected Graph Directed Graph Bipartite Graph
Binary Graph UBCM DBCM BiCM
Weighted Graph UECM, CReMa DECM, CReMa -

The BiCM module is also available as a standalone package, find its docs here.


  • [1] Squartini, Tiziano, Rossana Mastrandrea, and Diego Garlaschelli. "Unbiased sampling of network ensembles." New Journal of Physics 17.2 (2015): 023052.
  • [2] Parisi, Federica, Tiziano Squartini, and Diego Garlaschelli. "A faster horse on a safer trail: generalized inference for the efficient reconstruction of weighted networks." New Journal of Physics 22.5 (2020): 053053.
  • [3] Saracco, Fabio, Riccardo Di Clemente, Andrea Gabrielli, and Tiziano Squartini. "Randomizing bipartite networks: the case of the World Trade Web." Scientific reports 5, no. 1 (2015): 1-18.


NEMtropy can be installed via pip. You can get it from your terminal:

    $ pip install NEMtropy

If you already install the package and wish to upgrade it, you can simply type from your terminal:

    $ pip install NEMtropy --upgrade


NEMtropy uses numba and powerlaw libraries. They can be installed via pip by running in your terminal the following command:

    $ pip install numba
    $ pip install powerlaw

For python3.5 users the correct command is the following:

    $ pip install --prefer-binary numba

It avoids an error during the installation of llvmlite due to the absence of its wheel in python3.5.

Simple Example

As an example we solve the UBCM for zachary karate club network.

    import numpy as np
    import networkx as nx
    from NEMtropy import UndirectedGraph

    G = nx.karate_club_graph()
    adj_kar = nx.to_numpy_array(G)
    graph = UndirectedGraph(adj_kar)


Given the UBCM model, we can generate ten random copies of zachary's karate club.

    graph.ensemble_sampler(10, cpu_n=2, output_dir="sample/")

These copies are saved as an edgelist, each edgelist can be converted to an adjacency matrix by running the NEMtropy build graph function.

    from NEMtropy.network_functions import build_adjacency_from_edgelist

    edgelist_ens = np.loadtxt("sample/0.txt")
    ens_adj = build_adjacency_from_edgelist(edgelist = edgelist_ens,
                                            is_directed = False,
                                            is_sparse = False,
                                            is_weighted = False)

These collections of random adjacency matrices can be used as a null model: it is enough to compute the expected value of the selected network feature on the ensemble of matrices and to compare it with its original value.

To learn more, please read the ipython notebooks in the examples directory:


You can find complete documentation about NEMtropy library in docs.


Please work on a feature branch and create a pull request to the development branch. If necessary to merge manually do so without fast-forward:

    $ git merge --no-ff myfeature

To build a development environment run:

    $ python3 -m venv venv 
    $ source venv/bin/activate 
    $ pip install -e '.[dev]'


If you want to test the package integrity, you can run the following bash command from the tests' directory:

    $ bash

P.S. at the moment there may be some problems with the DECM solver functions



Nicolò Vallarano (a.k.a. nicoloval)

Emiliano Marchese (a.k.a. EmilianoMarchese)

Matteo Bruno (BiCM) (a.k.a. mat701)


The module was developed under the supervision of Tiziano Squartini, Fabio Saracco, Mario Zanon, and Giulio Cimini. It was developed at IMT school of advanced studies Lucca, and financed by the research project Optimized Reconstruction of Complex networkS - ORCS.

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