Consistent Community Detection in Continuous-Time Networks of Relational Events

In many application settings involving networks, such as messages between users of an on-line social network or transactions between traders in financial markets, the observed data are in the form of relational events with timestamps, which form a continuous-time network. We propose the Community Hawkes Independent Pairs (CHIP) model for community detection on such timestamped relational event data. We demonstrate that applying spectral clustering to adjacency matrices constructed from relational events generated by the CHIP model provides consistent community detection for a growing number of nodes. In particular, we obtain explicit non-asymptotic upper bounds on the misclustering rates based on the separation conditions required on the parameters of the model for consistent community detection. We also develop consistent and computationally efficient estimators for the parameters of the model. We demonstrate that our proposed CHIP model and estimation procedure scales to large networks with tens of thousands of nodes and provides superior fits compared to existing continuous-time network models on several real networks.