Collaboration and followership: a stochastic model for activities in social networks

In this work we investigate how future actions are influenced by the previous ones, in the specific contexts of scientific collaborations and friendships on social networks. We are not interested in modeling the process of link formation between the agents themselves, we instead describe the activity of the agents, providing a model for the formation of the bipartite network of actions and their features. Therefore we only require to know the chronological order in which the actions are performed, and not the order in which the agents are observed. Moreover, the total number of possible features is not specified a priori but is allowed to increase along time, and new actions can independently show some new entry features or exhibit some of the old ones. The choice of the old features is driven by a degree-fitness method. With this term we mean that the probability that a new action shows one of the old features does not solely depend on the "popularity" of that feature (i.e. the number of previous actions showing it), but is also affected by some individual traits of the agents or the features themselves, synthesized in certain quantities, called "fitnesses" or "weights", that can have different forms and different meaning according to the specific setting considered. We show some theoretical properties of the model and provide statistical tools for the parameters' estimation. The model has been tested on three different datasets and the numerical results are provided and discussed.