Online Social Networks (OSNs) have been the subject of a great deal of study in recent years. The majority of this study has used simple models, such as node-and-edge graphs, to describe the data. In this paper, we argue that such models, which necessarily limit the structures that can be described and omit temporal information, are insufficient to describe and study OSNs. Instead, we propose ... [Show full abstract] that a richer class of Entity Interaction Network models should be adopted. We outline a checklist of features that can help build such a model, and apply it to three popular networks (Twitter, Facebook and YouTube) to highlight important features. We also discuss important considerations for the collection, validation and sharing of OSN data.