  In this paper we model user behaviour in Twitter to capture the emergence of
trending topics. For this purpose, we first extensively analyse tweet datasets
of several different events. In particular, for these datasets, we construct
and investigate the retweet graphs. We find that the retweet graph for a
trending topic has a relatively dense largest connected component (LCC). Next,
based on the insights obtained from the analyses of the datasets, we design a
mathematical model that describes the evolution of a retweet graph by three
main parameters. We then quantify, analytically and by simulation, the
influence of the model parameters on the basic characteristics of the retweet
graph, such as the density of edges and the size and density of the LCC.
Finally, we put the model in practice, estimate its parameters and compare the
resulting behavior of the model to our datasets.
