to the large datasets considered. We use the same number of MCMC samples as for our model for each step.

We compare the different algorithms on link prediction. For each dataset, we make a train-test split in time so that the training datasets contains $85 \%$ of the total temporal interactions. We use the training data for parameter learning and then use the estimated parameters to perform link prediction on the held out test data. We report the root mean square error between the predicted and true number of interactions for each directed pair in the test set . The results are reported in Table \[tab:results\_and\_prop\]. On all the datasets, the proposed Hawkes-CCRM approach outperforms other methods. Interestingly, the addition of the Hawkes component brings improvement for both the IRM-based model and the CCRM-based model.

**Community structure, degree distribution and sparsity.** Our model also estimates the latent structure in the data through the weights $w_{ik}$, representing the level of affiliation of a node $i$ to a community $k$. For each dataset, we order the nodes by their highest estimated feature weight, obtaining a clustering of the nodes. We represent the ordered matrix $\left(z_{ij}\left(T\right)\right)$ of binary interactions in Figure \[fig:adjacency\] (a)-(d). 