## An Analysis of Delta Route Maps

(Click image to enlarge)

This is an example of a transportation network, in which nodes are cities in the United States, and the edges represent Delta Airlines routes. Although the graph of the Delta Airlines routes seems “connected,” it is not because not all cities in the United States have airports. There are some prominent central nodes that include Salt Lake City, St. Paul, Detroit, Atlanta, and New York. The graph can be divided into two big components: West(Seattle, Salt Lake City, Los Angeles) and East(Detroit, Atlanta, New York, and St. Paul). The edge between Salt Lake City and Atlanta(or Detroit) can be seen as a bridge since removal of the edge between those two cities would segregate many cities.

1973

1974

Although this is not a social network, some principles of social network such as triadic closure may apply. According to Triadic Closure principle, if two nodes have a friend in common, then there is a high chance that they will become friends. Moreover, if there are many friends in common, the two will more likely to become friends than those who lack or have fewer friends in common. For example, in 1973, there was no direct route between Chicago and New Orleans, but they had many “neighbors (like friends in social network)” in common such as Nashville, Binghamton, Atlanta, Memphis, and Houston. The next year (in 1974), a direct route (edge) was made between Chicago and New Orleans. On the other hand, in 1973, Chicago and San Diego did not have any “neighbors” in common, and there is no still Delta Airlines nonstop flight between Chicago and San Diego.

Since strong ties indicate great frequency of interaction, the strength of ties in the Delta Airlines Network can be determined by the frequency of flights among cities. The Strong Triadic Closure property suggests that if A has edges to B and C, and A forms strong ties with both B and C, then an edge between B and C is more likely to form. This property can be explained through the examples of Chicago-Kansas City and Chicago-New York. In Delta Airlines route map of 1974, there was no direct route(edge) between Chicago-Kansas City and Chicago-New York. The graph of 1974 also shows that Both Kansas City and New York share Atlanta with Chicago as their “neighbor” in common, and it was true that there was more frequency of flight in New York-Atlanta than that in Kansas City-Atlanta. Consequently, the edge between New York and Chicago was created while there is still no direct flight of Delta Airlines between Chicago and Kansas City.

One may see these Delta Airlines route maps and only say, “Wow so complicated.” However, these maps not only show examples of transportation networks, but also demonstrate several significant principles of network such as the Strong Triadic Closure property. Networks are ubiquitous!

http://www.delta.com/content/dam/delta-www/pdfs/route-maps/us-route-map.pdf

http://www.departedflights.com/DL030173.html

http://www.departedflights.com/DL102774.html