NEMtropy documentation

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},

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]

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

Binary Graph



Weighted Graph




  • [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.


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 library. It can be installed via pip by running in your terminal the following command:

$ pip install numba

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 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_graph_from_edgelist

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

These collection 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 two ipython notebooks in the examples directory: one is a study case on a directed graph, while the other is on an undirected graph.


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

Indices and tables