Complex systems are important when representing empirical systems in that they can model the underlying structure of interactions. Accounting for this structure can offer important insights for empirical systems such as social networks, biological processes, social phenomena, opinion formation, and many other examples. Pairwise networks are a representation of complex systems comprising a collection of entities (nodes) and pairwise interactions between entities (edges). Hypergraphs are a generalization of pairwise networks where interactions are no longer constrained to be between two nodes, but rather can be of arbitrary size. Modeling dynamics on hypergraphs can uncover rich behavior that one might not see if the dynamics simply occurred on a pairwise network. We focus on the interplay between the structure of a complex system, a particular dynamical process, and the resulting dynamical behavior. In the context of hypergraphs, we explain the effects that degree heterogeneity, assortative mixing, and community structure have on a simple hypergraph contagion model. Likewise, for pairwise networks, we explore both types of structure; structure in the underlying contact network and varying heterogeneity in the infection model. We examine the effect that representing inherently multiplex data (relationships of different types) with uniplex networks (relationships of a single type) has on the resulting dynamical behavior. We present two open source software libraries: (1) XGI, a package for representing complex systems with group interactions and (2) HyperContagion, a package for simulating hypergraph contagion, both of which can be used by the growing community of researchers studying higher-order interactions
