The clustering attachment (CA) is an evolution model of random graphs. In contrast to preferential attachment, the CA leads to a light-tailed node degree distribution and clusters of exceedances of the modularity over a sufficiently high threshold. The modularity shows the connectivity of nodes and serves to divide graphs into communities. An extremal index approximates the mean cluster size of exceedances over a high threshold. Considering the change of the modularity at each evolution step, the extremal index of the modularity random sequence indicates the consecutive large connectivity of nodes. It reflects the community appearance during the evolution. Our simulation shows how parameters of the CA model impact on the bursts of the modularity. The comparison of the CA evolution without and with node and edge deletion is provided.