Modeling temporal event sequences on the vertices of a network is an important problem with widespread applications; examples include modeling influences in social networks, preventing crimes by modeling their space–time occurrences, and forecasting earthquakes. Existing solutions for this problem use a parametric approach, whose applicability is limited to event sequences following some well-known distributions, which is not true for many real life event datasets. To overcome this limitation, in this work, we propose a composite recurrent neural network model for learning events occurring in the vertices of a network over time. Our proposed model combines two long short-term memory units to capture base intensity and conditional intensity of an event sequence. We also introduce a second-order statistic loss that penalizes higher divergence between the generated and the target sequence's distribution of hop count distance of consecutive events. Given a sequence of vertices of a network in which an event has occurred, the proposed model predicts the vertex where the next event would most likely occur. Experimental results on synthetic and real-world datasets validate the superiority of our proposed model in comparison to various baseline methods.