to capture the community structure together with a Hawkes process to capture reciprocity, (iii) the same model, called Poisson-IRM, without the Hawkes component, (iv) a simple Hawkes model where the conditional intensity given by Equation is assumed to be same for each pair of individuals, with unknown parameters $\delta$ and $\eta$, (v) a simple Poisson process model, which assumes that interactions between two individuals arise at an unknown constant rate. Each of these competing models capture a subset of the features we aim to capture in the data: sparsity/heterogeneity, community structure and reciprocity, as summarized in Table \[tab:results\_and\_prop\]. The models are given in the supplementary material. The only model to account for all the features is the proposed Hawkes-CCRM model.

  ------------- ------------- ------------- ------------- -------------
                                                          
                    email        college        math         ubuntu
  Hawkes-CCRM     **10.95**     **1.88**      **20.07**     **29.1**
  CCRM             $12.08$       $ 2.90$       $89.0$        $36.5$
  Hawkes-IRM       $14.2$        $ 3.56$        96.9          59.5
  Poisson-IRM      $31.7$        $15.7$         204.7         79.3
  Hawkes           $154.8$      $153.29$       220.10        191.39
  Poisson        $\sim10^ 3$   $ \sim10^4$   $ \sim10^4$   $\sim10^4 $
  ------------- ------------- ------------- ------------- -------------

  : (Left) Performance in link prediction. (Right) Properties captured by the different models.

\[tab:results\_and\_prop\]

[c@c@c@]{} sparsity/ & community & reciprocity\
heterogeneity & structure\
& &\
& &\
&&\
&&\
& 