Decentralized social media platforms like Bluesky Social (Bluesky) have made it possible to publicly disclose some user behaviors with millisecond-level precision. Embracing Bluesky's principles of open-source and open-data, we present the first collection of the temporal dynamics of user-driven social interactions. BlueTempNet integrates multiple types of networks into a single multi-network, including user-to-user interactions (following and blocking users) and user-to-community interactions (creating and joining communities). Communities are user-formed groups in custom Feeds, where users subscribe to posts aligned with their interests. Following Bluesky's public data policy, we collect existing Bluesky Feeds, including the users who liked and generated these Feeds, and provide tools to gather users' social interactions within a date range. This data-collection strategy captures past user behaviors and supports the future data collection of user behavior.
A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, the true connections consist of events arriving as streams, which are then aggregated to form edges, ignoring the dynamic temporal component. A natural way to take account of these temporal dynamics of interactions is to use point processes as the foundation of network models for community detection. Computational complexity hampers the scalability of such approaches to large sparse networks. To circumvent this challenge, we propose a fast online variational inference algorithm for estimating the latent structure underlying dynamic event arrivals on a network, using continuous-time point process latent network models. We describe this procedure for networks models capturing community structure. This structure can be learned as new events are observed on the network, updating the inferred community assignments. We investigate the theoretical properties of such an inference scheme, and provide regret bounds on the loss function of this procedure. The proposed inference procedure is then thoroughly compared, using both simulation studies and real data, to non-online variants. We demonstrate that online inference can obtain comparable performance, in terms of community recovery, to non-online variants, while realising computational gains. Our proposed inference framework can also be readily modified to incorporate other popular network structures.