Many networks such as communication, social media, covert and criminal networks have event-driven dynamics where the intensity rate of the events changes according to the occurrences of events in the network. In particular, events that occurred in a node of the network could increase the intensity of other nodes depending on their causal relationship. Thus, it is of interest to use data to uncover the influence network in which the edges represent the directional influence between nodes. An event-driven dynamic on a network can be modelled by a multi-dimensional Hawkes process driven by count data. In this setting, the influence structure of the network is then parameterized by the Hawke process. Understanding the uncertainty of the network constructed from the data is also important. This talks will discuss how we may build an ensemble of networks to reflect uncertainty. The outcome will facilitate downstream uncertainty analysis for network applications such as node classifications, link prediction and rare-event detection.