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We propose a novel sequence prediction method for sequential data capturingnode traversals in graphs. Our method builds on a statistical modellingframework that combines multiple higher-order network models into a singlemulti-order model. We develop a technique to fit such multi-order models inempirical sequential data and to select the optimal maximum order. Ourframework facilitates both next-element and full sequence prediction given asequence-prefix of any length. We evaluate our model based on six empiricaldata sets containing sequences from website navigation as well as publictransport systems. The results show that our method out-performsstate-of-the-art algorithms for next-element prediction. We further demonstratethe accuracy of our method during out-of-sample sequence prediction andvalidate that our method can scale to data sets with millions of sequences.

Predicting Sequences of Traversed Nodes in Graphs using Network Models with Multiple Higher Orders