If you work, study or play in network science then chances are you have generated a network. Whether or not you have a real-world system to analyse, synthetic networks play an important role in network science. Generating networks of a chosen size can provide a null model for a statistical test, a test bed for new algorithms or the basis for studying the interplay between structure and dynamics in complex systems. Consequently network science literature contains a wide array of network models: some designed as processes to replicate observed properties and others for the purposes of statistical inference. However, these models have different parameters and constraints associated with their generative models, may or may not have the ability to control for random noise and do not always have readily available software implementations, thus making them unavailable to network science practitioners.

The article of Cazabet et al. (2023) introduces a software "zoo, " called Structify-Net, that contains a range of models that the authors have captured from the wild. The authors have focused on developing a framework that enables the generation networks of a chosen size, according to number of nodes and edges, and provides the means to control for randomness, by interpolating between the specified structure and a random graph. The article also discusses an interesting use case to examine the interplay between network structure and node attributes, which might compliment methods based on permutation tests (Bianconi et al. 2009, Ehrhardt and Wolfe 2019). 

Structify-Net presents some interesting future opportunities. For instance, the independence that Structify-Net imposes on edge ranking (defined by the model) and the expected number of edges (defined by the user) might offer a route towards exploring network growth or evolution. Like any zoo Structify-Net is not complete in that there are many more exotic "species" that the authors, or perhaps others in the network science community, may later collect. Collecting more model implementations to align with reviews of network models (Goldenberg et al. 2010) together with methods of statistical inference has the potential to lay the foundations for the ever important bridge between theory and practice in network science (Peel et al. 2022).

References

Bianconi, Ginestra, Paolo Pin, and Matteo Marsili (2009) Assessing the Relevance of Node Features for Network Structure. Proceedings of the National Academy of Sciences 106, 28: 11433–38. https://doi.org/10.1073/pnas.0811511106

Cazabet, Remy, Salvatore Citraro, and Giulio Rossetti (2023) Structify-Net: Random Graph Generation with Controlled Size and Customized Structure. arXiv, ver. 2 peer-reviewed and recommended by Peer Community in Network Science. https://doi.org/10.48550/arXiv.2306.05274

Ehrhardt, Beate, and Patrick J. Wolfe (2019) Network Modularity in the Presence of Covariates’. SIAM Review 61, 2: 261–76. https://doi.org/10.1137/17M1111528

Goldenberg, Anna, Alice X. Zheng, Stephen E. Fienberg, and Edoardo M. Airoldi (2010) A Survey of Statistical Network Models. Foundations and Trends in Machine Learning 2, 2: 129–233. https://doi.org/10.1561/2200000005

Peel, Leto, Tiago P. Peixoto, and Manlio De Domenico (2022) Statistical Inference Links Data and Theory in Network Science. Nature Communications 13, 1: 6794. https://doi.org/10.1038/s41467-022-34267-9