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arXiv · 1705.10298

Construction of and efficient sampling from the simplicial configuration model

Jean-Gabriel Young·Giovanni Petri·Francesco Vaccarino·Alice Patania
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Abstract

Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multi-node interactions explicitly. With this new description comes the need for principled null models that allow for easy comparison with empirical data. We propose a natural candidate, the simplicial configuration model. The core of our contribution is an efficient and uniform Markov chain Monte Carlo sampler for this model. We demonstrate its usefulness in a short case study by investigating the topology of three real systems and their randomized counterparts (using their Betti numbers). For two out of three systems, the model allows us to reject the hypothesis that there is no organization beyond the local scale.

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Jean-Gabriel Young, Giovanni Petri, Francesco Vaccarino, Alice Patania. 2017-09-25. Construction of and efficient sampling from the simplicial configuration model. https://doi.org/10.1103/physreve.96.032312

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