A new theoretical framework makes it possible to model temporal hypergraphs whose activity does not follow Poisson statistics, a case that classical network approaches fail to capture well. The proposal describes the evolution of nodes through Markovian dynamics, so that group interactions —the hyperedges— emerge as a consequence of internal states that change over time.

Temporal hypergraphs extend traditional networks by allowing a single event to involve more than two nodes at once and by letting the connection structure change over time. Modelling them accurately is useful for describing real systems such as social interactions, biological processes or contagion dynamics, where events are not independent of one another and the distribution of times between them departs from the exponential form characteristic of a Poisson process.

The approach is based on associating a Markov process to each node, whose transitions govern when and with whom it interacts. By tuning the rates of these processes, the model reproduces waiting-time distributions with heavy tails and temporal correlations observed empirically, without needing to introduce ad hoc rules for each system.

The relevance of the work lies in offering a unified and analytically tractable framework for a broad class of network phenomena that until now required ad hoc descriptions. By connecting the microscopic dynamics of nodes with the global statistical properties of the hypergraph, the proposal opens the door to quantitative predictions about how complex collective systems evolve.