Network flow models in operations research

Abstract: An important problem that arises in the analysis of many complex networks is to identify the common pathways that enable the flow of information (or other quantities) through the network.

This is a particularly challenging problem when the only information observed consists of the timing of events in the network. We develop a framework based on multidimensional Hawkes processes that can be used to determine how events are related.

This extends the capability of Hawkes process-based models to infer how network events relate.

Network flow algorithm example

We then show how a simple dynamic program can exploit this data to recognize chains of events and provide a much deeper insight into the behavior of nodes within the network. Simulations are provided to demonstrate the capabilities and limitations of this framework.