The goal of the MaxEntropyGraphs.jl package is to group the various maximum-entropy null models for network randomization and make them available to the Julia community in a single package. This work was in part inspired by the Maximum Entropy Hub, but unlike the latter, this package works in an integrated way with the exisiting Julia ecosystem for handling graphs, optimization tools and numerical solvers and groups all models in a single framework.
The package provides the following functionalities:
- Computing the likelihood maximizing parameters for a broad set of network models (cf.
Modelssection of the documentation). - Sampling of networks from a network ensemble once the parameters have been computed.
- Analytically computing ensemble averages and their standard deviations (for a subset of models).
- Running motif based analysis (for a subset of models).
- Bipartite network projections with statistical significance analysis (for a subset of models).
Each network models can be solved in different ways, with a fixed-point method typically being the fastest and a Newton-based method being the slowest. Depending on the complexity of the network model, some solvers might not always converge.
Assuming that you already have Julia correctly installed, installation is straightforward. It suffices to import MaxEntropyGraphs.jl in the standard way:
using Pkg
Pkg.add("MaxEntropyGraphs")or enter the Pkg mode by hitting ], and then run the following command:
pkg> add MaxEntropyGraphsMore detailed information is available in the documentation and some demos are available in the examples subfolder.
using Graphs
using MaxEntropyGraphs
# generate a simple graph
G = smallgraph(:karate)
# generate a model
model = UBCM(G)
# solve the model
solve_model!(model)
# generate 100 random instances from the ensemble
G_sample = rand(model, 100)MaxEntropyGraphs.jl is intended to do network randomization. The specific kind of network to randomize and the properties to preserve defines the model you need.
Details for each of the available models can be found in the Models section.
Sometimes multiple models might be applicable. In that case, you can use information theory-based metrics to help make an informed decision.
The Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are available to quantify this.
Lower BIC or AIC values indicate a better model fit, considering the trade-off between complexity and fit.
When using this package for your scientific research please consider citing:
@software{bart_de_clerck_2023_8314610,
author = {Bart De Clerck},
title = {B4rtDC/MaxEntropyGraphs.jl: v0.3.2},
month = sep,
year = 2023,
publisher = {Zenodo},
version = {v0.3.2},
doi = {10.5281/zenodo.8314610},
url = {https://doi.org/10.5281/zenodo.8314610}
}
References
- [1] Squartini, Tiziano, Rossana Mastrandrea, and Diego Garlaschelli. "Unbiased sampling of network ensembles." New Journal of Physics 17.2 (2015): 023052. https://arxiv.org/abs/1406.1197
- [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. https://arxiv.org/abs/1811.09829
- [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. https://doi.org/10.1038/srep10595
- [4] Nicolò Vallarano, Matteo Bruno, Emiliano Marchese, Giuseppe Trapani, Fabio Saracco, Giulio Cimini, Mario Zanon & Tiziano Squartini Saracco, Fabio, Riccardo Di Clemente, Andrea Gabrielli, and Tiziano Squartini. "Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints." Scientific reports 11 (2021). https://doi.org/10.1038/s41598-021-93830-4