Subgraphs and motifs in a dynamic airline network

How does the small-scale topological structure of an airline network behave as the network evolves? To address this question, we study the dynamic properties of small undirected subgraphs using 15 years of data on Southwest Airlines' domestic route service. We use exact enumeration formulae to identify statistically over- and under-represented subgraphs, known as motifs and anti-motifs. We discover substantial topology transitions in Southwest's network and provide evidence for time-varying power-law scaling between subgraph counts and the number of edges in the network. We also suggest a node-ranking measure that can identify important nodes relative to specific local topologies. Our results extend the toolkit of subgraph-based methods and provide new insight into transportation networks and the strategic behaviour of firms.