• network
• network theory
• hypergraph
• hypergraph reconstruction
• statistical mechanics

We address the problem of inferencing higher-order interactions using information concerning pairwise connections within a network. In particular, we focus on hypergraphs encoding pairwise and three-node interactions, developing new models based on hypergraph formalism to represent such higher-order interactions.
We follow a Statistical Mechanics approach to extend two well-known models, namely the Erdös-Rényi model for homogenous graphs and the fitness model for heterogenous networks, to the hypergraph formalism.
Moreover, for the first time, we focus on the
correlation structure existing between pairwise and three-node connections, studying how much the graph of pairwise relations is informative for recovering the three-node interaction structure.
To this aim, we propose several variations of the hypergraph Erdös-Rényi enforcing a correlation among interactions of different orders.
Therefore, we assess each model's accuracy in recovering a tree-node interaction network by investigating a network of scientific collaborations in Computer Science.
A coauthorship network allows for directly measuring higher-order interactions as articles written by several authors can be interpreted as many-body interactions.
We measure each model's accuracy by comparing the higher-order interaction structure provided by each model with the measured one, observing some informative value concerning pairwise connections for predicting higher-order interactions.