Mining evolving network processes

Processes within real world networks evolve according to the underlying graph structure. A number of examples exists in diverse network genres: botnet communication growth, moving traffic jams [1], information foraging [2] in document networks (WWW and Wikipedia), and spread of viral memes or opinions in social networks. The network structure in all the above examples remains relatively fixed, while the shape, size and position of the affected network regions change gradually with time. Traffic jams grow, move, shrink and eventually disappear. Public attention shifts among current hot topics inducing a similar shift of highly accessed Wikipedia articles. Discovery of such smoothly evolving network processes has the potential to expose the intrinsic mechanisms of complex network dynamics, enable new data-driven models and improve network design. We introduce the novel problem of Mining smoothly evolving processes (MINESMOOTH) in networks with dynamic real-valued node/edge weights. We show that ensuring smooth transitions in the solution is NP-hard even on restricted network structures such as trees. We propose an efficient filtering based framework, called LEGATO. It achieves 3-7 times higher scores (i.e. larger and more significant processes) compared to alternatives on real networks, and above 80% accuracy in discovering realistic "embedded" processes in synthetic networks. In transportation networks, LEGATO discovers processes that conform to existing traffic jams models. Its results in Wikipedia reveal the temporal evolution of information seeking of Internet users.