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Moreover, ignoring interaction functions, we demonstrate rather simply that hypergraph structures are *generalized* by multilayer graphs. So even if you can't get over the fact that hypergraphs are just bipartite graphs dressed in uglier terminology, now you have something else to cope with. 11/N

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In fact, the phenomenology in question belongs to the same class of abrupt transitions present in bootstrap (k-core) percolation, and interdependent percolation—very well known graph models, unrelated to hypergraphs, but never referenced in the HON literature. 10/N

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Since graphs *constrain* rather than define the interactions, it follows that graph-based models *generalize* those based on hypergraphs! For a simple reason: Hypergraphs impose structure on the interactions that graph-based models leave open, making hypergraph models the more restrictive class. 6/N

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Tiago Peixoto @tiago.skewed.de · 29/01/2026

But this just isn't true. Graphs define neighborhoods, i.e. the set of nodes adjacent to a given node, not the interactions themselves. The functions defined on these neighborhoods can be arbitrarily complex and multivariate, depending on all adjacent nodes simultaneously in nonlinear ways. 4/N

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It's truly remarkable how blatant propaganda can be.

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Tiago Peixoto @tiago.skewed.de · 11/12/2025

It's like those movie posters where the billing order does not match the promotion material.

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Tiago Peixoto @tiago.skewed.de · 24/07/2025

I enjoyed visiting Florence for #STATPHYS29...

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Our approach is able to distinguish between posterior probabilities and weight magnitudes, something which is in general conflated with most other methods. We use this to compare our inferential reconstruction with those based on correlation thresholds. The discrepancy is massive! 9/N

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This allows us to probe the ensemble of reconstructions, like in the case of the network of influence between deputies in the Brazilian congress, based only on their voting patterns. 8/N

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The current work leverages on those developments to produce *samples* from the posterior distribution of reconstructed networks, according to their plausibilities, in a manner that also works for larger problem instances. 7/N

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Network reconstruction is needed when we do not have direct measurements on the network structure, only on the dynamics that it generates, or some other indirect data. It's an important problem, with direct relevance to ecology, neuroscience, epidemiology, and others. dx.doi.org/10.1038/s414... 2/N

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Tiago Peixoto @tiago.skewed.de · 05/02/2025

🚨 New paper on ArXiv: “Uncertainty quantification and posterior sampling for network reconstruction” TL;DR; We present an efficient method to sample the entire ensemble of possible network reconstructions that are compatible with an indirect observation, e.g. a dynamics. Short thread: 1/N

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Just a regular morning in Vienna...

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Tiago Peixoto @tiago.skewed.de · 19/12/2024

But the temperature is going up as the number of pirates go down!

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Tiago Peixoto @tiago.skewed.de · 19/12/2024

That's demonstrably false in a variety of easy examples.

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Tiago Peixoto @tiago.skewed.de · 19/12/2024

The number of pirates and the global temperature are clearly correlated, therefore they are “functionally connected”? What a completely pointless concept. Why not just say it's correlated and leave it at that? Why deny the obvious fact that FC is trying to claim something more profound?

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Tiago Peixoto @tiago.skewed.de · 02/12/2024

It uses C++ under the hood for the heavy lifting, making it quite fast. This version includes new features, bug fixes, and improved documentation: graph-tool.skewed.de/static/doc/ Did you know that you can infer network from dynamics using graph-tool? graph-tool.skewed.de/static/doc/d... 2/N

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Tiago Peixoto @tiago.skewed.de · 02/12/2024

Good news everyone! A new version of graph-tool is just out! @graph-tool.skewed.de graph-tool.skewed.de Graph-tool is a comprehensive and efficient Python library to work with networks, including structural, dynamical, and statistical algorithms, as well as visualization. 1/N #networkscience

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Tiago Peixoto @tiago.skewed.de · 15/10/2024

🚨Job alert!🚨 Come join us at the Inverse Complexity Lab! @invcomplexity.bsky.social We’re hiring a post-doctoral researcher to join our group at IT:U, Linz, Austria. skewed.de/lab/call.html Deadline is 30 Nov 2024. 1/8

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Tiago Peixoto @tiago.skewed.de · 26/09/2024

We're living in a cyberpunk reality, but a stupider, B-movie variety.

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Tiago Peixoto @tiago.skewed.de · 17/09/2024

These young kids need to get off my lawn...

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Tiago Peixoto @tiago.skewed.de · 06/05/2024

It uses C++ under the hood for the heavy lifting, making it quite fast. This version includes new features, bug fixes, and improved documentation: graph-tool.skewed.de/static/doc/ One of the new features is scalable and principled network reconstruction: graph-tool.skewed.de/static/doc/d... 2/N

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Tiago Peixoto @tiago.skewed.de · 06/05/2024

Good news everyone! A new version of graph-tool is just out! graph-tool.skewed.de graph-tool is a comprehensive and efficient Python library to work with networks, including structural, dynamical, and statistical algorithms, as well as visualization. 1/N

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Tiago Peixoto @tiago.skewed.de · 07/03/2024

Are you attending #netsci2024 and want to present your newest work on statistical network methods? Submit your talk to SINM: sinm.network We have excellent speakers: Roger Guimerà, Matthew Eichhorn, and Zachary Lubberts (and more!) Submission deadline is April 1st.

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Tiago Peixoto @tiago.skewed.de · 08/01/2024

We're hiring! Tenure-track Assistant Professor at DNDS, CEU, in Vienna, Austria! The focus is on social data science, social network science, or quantitative social science — broadly interpreted. Deadline: February 20, 2024 For questions, get in touch! www.ceu.edu/job/assistan...

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The end result is that we can reconstruct networks with hundreds of thousands and even millions of nodes and edges! Below is a reconstructed network from the co-occurrence of N=317,314 microbial species sampled on the entire planet. Can you imagine doing this with GLASSO? 9/N

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The speedup over the quadratic baseline can be in the order of 10³ already for networks with N=10⁴ nodes, and this gap only increases for larger N. Plus: The algorithm is easily parallelizable and will use any number of threads you can give to it! 8/N

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As a result, we can find out which edges we should add/remove to the reconstruction in log-linear time, instead of quadratic! 7/N

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