Sequential Motifs in Observed Walks

TL;DR

This paper introduces a method to identify and analyze sequential motifs in trajectory data, linking them to higher-order network models, and demonstrates its effectiveness on transportation and information networks.

Contribution

It defines sequential motifs in trajectory data and connects their analysis to higher-order network models, enabling counting and importance evaluation in observed sequences.

Findings

Prevalent motifs align with intuitive traversal patterns.

Heterogeneity in edge weights affects motif distribution.

Method applied successfully to airport and Wikipedia networks.

Abstract

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