Epidemic Spreading on Directed Networks and Twitter Cascades

The development of models for social networks and the spread of information therein has become an important field of research in recent decades. Here we apply and adapt recent results from the theory of heterogeneous random graphs to the problem of modelling Twitter networks and predicting the size of Twitter cascades. We show that the size of a Twitter cascade (measured by the number of users which have retweeted a tweet) can be linked to the size of the largest forward connected component in heterogeneous, directed random graph models with independent edges. We discuss different specifications of such random graph models for real Twitter networks and compare their predictive power when comparing virtual Twitter cascades on real Twitter networks with cascades on random graph based networks. We find that kernel based random graph models which properly present the joint in- and out-degree distribution, have the best match with real Twitter networks. Although the considered random graph models have by construction only a small number of triangles in comparison to real Twitter networks, we find good agreement when comparing cascade sizes and obtain the prediction error to be significantly less compared to the state-of-the-art. Our results show that sophisticated recent random graph theories provide a very interesting and novel modelling approach for a larger variety of spreading processes and should become more widely known.