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Abstract 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.