  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 consist of timestamped relational events, which form
a continuous-time network. We propose the Community Hawkes Independent Pairs
(CHIP) generative model for such networks. We show that applying spectral
clustering to an aggregated adjacency matrix constructed from the CHIP model
provides consistent community detection for a growing number of nodes and time
duration. We also develop consistent and computationally efficient estimators
for the model parameters. We demonstrate that our proposed CHIP model and
estimation procedure scales to large networks with tens of thousands of nodes
and provides superior fits than existing continuous-time network models on
several real networks.
