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Network modeling characterizes the underlying principles of structuralproperties and is of vital significance for simulating dynamical processes inreal world. However, bridging structure and dynamics is always challenging dueto the multiple complexities in real systems. Here, through introducing theindividual's activity rate and the possibility of group interaction, we proposea probabilistic activity driven (PAD) model that could generate temporalhigher-order networks with both power-law and high-clustering characteristics,which successfully links the two most critical structural features and a basicdynamical pattern in extensive complex systems. Surprisingly, the power-lawexponents and the clustering coefficients of the aggregated PAD network couldbe tuned in a wide range by altering a set of model parameters. We furtherprovide an approximation algorithm to select the proper parameters that cangenerate networks with given structural properties, the effectiveness of whichis verified by fitting various real-world networks. Lastly, we explore theco-evolution of PAD model and higher-order contagion dynamics, and analyticallyderive the critical conditions for phase transition and bistable phenomenon.Our model provides a basic tool to reproduce complex structural properties andto study the widespread higher-order dynamics, which has great potential forapplications across fields.

Probabilistic activity driven model of temporal simplicial networks and its application on higher-order dynamics