• attributed stream-hypergraph
• high-order networks
• social networks analysis
• temporal networks

Graphs are simple, intuitive proxies that allow for an effective modeling of many complex systems. Although functional, however, such simplicity imposes strong constraints on the system's representation. Indeed, many real world phenomena present much more than a relational structure, such as a wide set of attributes characterizing the entities and/or time-varying topologies. Additionally, relations may involve more than two entities at once, whereas graphs are intrinsically limited to pairwise interactions. These are pivotal features of any complex systems – especially social ones – and must be taken into account in order to deploy understand the systems’ nature.
In this work, an all-encompassing framework is proposed, namely the Attributed Stream-Hypergraph (ASH). Leveraging powerful and well-understood models such as hypergraphs and stream graphs, ASH frames systems as a stream of node-attributed multiadic interactions. By doing so, it is able to provide novel insights that the original models are not able to unveil independently.
After discussing other augmented graph models concerning attributed, temporal, and high-order networks, ASH is presented along with its analytical peculiarities and measures. A Python implementation of the model is also discussed and compared to other hypergraph libraries, emphasizing pros and cons of each. Lastly, ASH is leveraged to study both online and offline complex social systems, including Reddit mental health and political discussion boards, and face-to-face interactions in primary and high schools.