Nicolò Ruggeri, Alessandro Lonardi and Caterina De Bacco
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Message-passing on hypergraphs: detectability, phase transitions and higher-order information
Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits. Here, we derive closed-form bounds for community detection in hypergraphs. Using a message-passing formulation, we demonstrate that detectability depends on the hypergraphs’ structural properties, such as the distribution of hyperedge sizes or their assortativity. Our formulation enables a characterization of the entropy of a hypergraph in relation to that of its clique expansion, showing that community detection is enhanced when hyperedges highly overlap on pairs of nodes. We develop an efficient message-passing algorithm to learn communities and model parameters on large systems. Additionally, we devise an exact sampling routine to generate synthetic data from our probabilistic model. Using these methods, we numerically investigate the boundaries of community detection in synthetic datasets, and extract communities from real systems. Our results extend our understanding of the limits of community detection in hypergraphs and introduce flexible mathematical tools to study systems with higher-order interactions.
期刊介绍:
JSTAT is targeted to a broad community interested in different aspects of statistical physics, which are roughly defined by the fields represented in the conferences called ''Statistical Physics''. Submissions from experimentalists working on all the topics which have some ''connection to statistical physics are also strongly encouraged.
The journal covers different topics which correspond to the following keyword sections.
1. Quantum statistical physics, condensed matter, integrable systems
Scientific Directors: Eduardo Fradkin and Giuseppe Mussardo
2. Classical statistical mechanics, equilibrium and non-equilibrium
Scientific Directors: David Mukamel, Matteo Marsili and Giuseppe Mussardo
3. Disordered systems, classical and quantum
Scientific Directors: Eduardo Fradkin and Riccardo Zecchina
4. Interdisciplinary statistical mechanics
Scientific Directors: Matteo Marsili and Riccardo Zecchina
5. Biological modelling and information
Scientific Directors: Matteo Marsili, William Bialek and Riccardo Zecchina