Tom Britton: Directed preferential attachment networks

Abstract:
The original preferential attachment model for an undirected network was 10 years ago generalized to a directed network model, where nodes together with out- (in-) directed edges appear sequentially, and where the probability to attach to a given node is proportional to the in- (out-) degree of that node. The bivariate degree distribution is defined as the in- and out-degree of a randomly selected node. In the talk we analyse the model using a new approach where it is shown that the distribution can be characterized by two independent birth processes observed at a common exponentially distributed time-point. The method is easily extended to more realistic models allowing for doubly-directed edges as well as attachment probabilities depending both on in- and out-degree.