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 and spatial properties of small undirected subgraphs using 15 years of data on Southwest Airlines' domestic route service. We find that this real-world network has much in common with random graphs, and describe a possible power-law scaling between subgraph counts and the number of edges in the network, that appears to be quite robust to changes in network density and size. We use analytic formulae to identify statistically over-and under-represented subgraphs, known as motifs and anti-motifs, and discover the existence of substantial topology transitions. We propose a simple subgraph-based node ranking measure, that is not always highly correlated with standard node centrality, and can identify important nodes relative to specific topologies; and investigate the spatial "distribution" of the triangle subgraph using graphical tools. Our results have implications for the way in which subgraphs can be used to analyze real-world networks. * We are grateful to Karim Abadir, Gergana Bounova, Pascal Lezaud, Chantal Roucolle and Miguel Urdanoz for helpful comments and suggestions. We also thank Patrick Senac for supporting this project: Agasse-Duval was partially funded by an ENAC summer research grant. Correspondence can be addressed to Steve Lawford, ENAC (DEVI),. The visualization, subgraph analysis, and motif detection tools used in this paper were coded by the authors in Python 2.7. The usual caveat applies.