New paper. With Ekaterina Vasileva, Liubov Tupikina, Dmitry Fedorov, Daniil Musatov, Andrei Raigorodskii and Stefano Boccaletti.

The naive generalization of the concept of distance to hypergraphs is equivalent to applying a clique-projection approximation. However, this is known to induce loss of information, especially in networks where the higher-order interactions are very important. To fix this problem,we introduce a new definition of distance on weighted higher-order networks, which includes the case of unweighted hypergraphs and classic graph distance as particular cases, and allows one to account for different meanings associated to the weights. We also show what difference this makes in analyses of real-world data.

https://www.nature.com/articles/s42005-026-02592-w

#mathematics #physics #graphtheory #graphs #hypergraphs #higherordernetworks #networkscience #networks

🧠 New preprint on adaptive contagion dynamics on #hypergraphs by Mancastroppa, Karsai, & Barrat.

The key result: adaptive, locally informed behavior can neutralize explosive phase transitions in higher-order contagion. Group-level awareness suppresses nonlinear reinforcement, shrinks bistability, and can turn a discontinuous transition into a continuous one. A nice mechanistic link between adaptivity, higher-order interactions, and phase transitions.

#ComplexSystems #NonlinearDynamics

#mathstodon #graphTheory
I am working on writing a GUI for editing edge-representation #Hypergraphs Anyone played with drawing these? I have a couple of ways of approaching this, and would like to choose something useful and useable beyond just my rather narrow experience and application.

I am writing in #Python using #pyside6 and can (within reason!) make it do what is best for editing and thinking.

Any links/ references/ resources/ boosts welcome.

New paper!
How can we detect the presence of communities in networks with higher-order interactions? For instance, by maximizing hypermodularity! Also, this formulation will allow you to leverage tensor spectral methods to do it. Additionally, the paper also argues that the "overfitting" of modularity methods is actually just people applying them where they are not supposed to be used. And, as a byproduct, there is an explanation of why higher-order SVD works so well in classification tasks in machine learning. Oh, the code is available to use in your own projects (link in the first comment). And moreover, the code includes an efficient data structure for higher-order networks that is independent from the community detection method and that you can also use in your own work. 😎

https://journals.aps.org/prresearch/abstract/10.1103/58dr-wktc

#networks #complexity #physics #maths #CompSci #graphs #higherorder #hypergraphs #community #detection #algorithm #communitystructure #modularity #hypermodularity

All those who couldn't join us in Natal for the International School and Workshop in Complex Networks Beyond Pairwise Interactions can still access all the lectures and talks, courtesy of the International Institute of Physics! 😎

- Fundamental definitions and properties
- Dynamical processes
- Synchronisation
- Control
- Belief propagation
- Community detection

and more!

Please boost to reach the largest possible audience.

https://www.youtube.com/playlist?list=PLqTLz9G2bGs2-ToEsAuUg3u6ZASY1UbAk

#mathematics #physics #structure #dynamics #complexity #science #networks #graphs #hypergraphs #school #workshop #conference #natal #riograndedonorte #brazil #UFRN

New paper, just out.

Often, in real-world situations, one does not know the full structure of a network. However, at the same time, one can often observe some interactions that take place on it, and may be interested in knowing its full structure. For example, one may be detecting some partial criminal activity and may want to determine the whole organization. We consider higher-order networks, which are structures with many-body interactions, and specifically simplicial complexes, and show that one can reconstruct a whole network almost perfectly simply by observing the transient of the dynamics that takes place on it. In fact, we give 3 different algorithms to do it, with different complexities and accuracies, so you can choose which one suits you best.

#physics #mathematics #networks #reconstruction #higherorder #simplicialcomplex #hypergraphs #evolutionarygames #transient #dynamics #algorithm