Sequential motifs in observed walks

Abstract The structure of complex networks can be characterized by counting and analysing network motifs. Motifs are small graph structures that occur repeatedly in a network, such as triangles or chains. Recent work has generalized motifs to temporal dynamic data. However, existing techniques do not generalize sequential trajectory data, which represent entities moving through the nodes passengers transportation networks. unit observation these data is fundamentally different since we analyse observations trajectories (e.g. trip from airport A C B), rather than independent edges snapshots graphs over time. In this work, define small, directed sequence-ordered corresponding patterns observed sequences. We draw connection between analysis Higher-Order Network (HON) models. show mapping HON, specifically $k$th-order DeBruijn graph, motifs, count evaluate their importance test our methodology with two datasets: (1) navigating an (2) people Wikipedia article network. find most prevalent important correspond intuitive traversal real systems empirically heterogeneity edge weights higher-order implications for distributions expect see across null