  The application of network analysis has found great success in a wide variety
of disciplines; however, the popularity of these approaches has revealed the
difficulty in handling networks whose complexity scales rapidly. One of the
main interests in network analysis is the online detection of anomalous
behaviour. To overcome the curse of dimensionality, we introduce a network
surveillance method bringing together network modelling and statistical process
control. Our approach is to apply multivariate control charts based on
exponential smoothing and cumulative sums in order to monitor networks
determined by temporal exponential random graph models (TERGM). This allows us
to account for temporal dependence, while simultaneously reducing the number of
parameters to be monitored. The performance of the proposed charts is evaluated
by calculating the average run length for both simulated and real data. To
prove the appropriateness of the TERGM to describe network data, some measures
of goodness of fit are inspected. We demonstrate the effectiveness of the
proposed approach by an empirical application, monitoring daily flights in the
United States to detect anomalous patterns.
