  This paper introduces graph-based mutually exciting processes (GB-MEP) to
model event times in network point processes, focusing on an application to
docked bike-sharing systems. GB-MEP incorporates known relationships between
nodes in a graph within the intensity function of a node-based multivariate
Hawkes process. This approach reduces the number of parameters to a quantity
proportional to the number of nodes in the network, resulting in significant
advantages for computational scalability when compared to traditional methods.
The model is applied on event data observed on the Santander Cycles network in
central London, demonstrating that exploiting network-wide information related
to geographical location of the stations is beneficial to improve the
performance of node-based models for applications in bike-sharing systems. The
proposed GB-MEP framework is more generally applicable to any network point
process where a distance function between nodes is available, demonstrating
wider applicability.
