Network Analysis of World Subway Systems Using Updated Graph Theory

Document Type

Journal Article

Publication Date


Subject Area

infrastructure - interchange/transfer, planning - network design, land use - planning, ridership - commuting, mode - rail, mode - mass transit, mode - subway/metro


Washington (District of Columbia), Underground railways, Transit connectivity, Transit, Transfers, Toronto (Canada), Tokyo (Japan), Subways, Stockholm (Sweden), Singapore, Service coverage, Seoul (Korea), San Francisco (California), Ridership, Public transit, Patronage (Transit ridership), Paris (France), Osaka (Japan), New York City, New York (New York), Network design, Network analysis (Planning), Multiple regression analysis, Moscow (Russia), Montreal (Canada), Mobility, Mexico City (Mexico), Mass transit, Madrid (Spain), Lyons (France), Lyon (France), London (England), Local transit, Graph theory, Chicago (Illinois), Berlin (Germany), Athens (Greece)


This paper demonstrates that network topologies play a key role in attracting people to use public transit; ridership is not solely determined by cultural characteristics (North American versus European versus Asian) or city design (transit oriented versus automobile oriented). The analysis considers 19 subway systems worldwide: those in Toronto, Ontario, Canada; Montreal, Quebec, Canada; Chicago, Illinois; New York City; Washington, D.C.; San Francisco, California; Mexico City, Mexico; London; Paris; Lyon, France; Madrid, Spain; Berlin; Athens, Greece; Stockholm, Sweden; Moscow; Tokyo; Osaka, Japan; Seoul, South Korea; and Singapore. The relationship between ridership and network design was studied by using updated graph theory concepts. Ridership was computed as the annual number of boardings per capita. Network design was measured according to three major indicators. The first is a measure of transit coverage and is based on the total number of stations and land area. The second relates to the maximum number of transfers necessary to go from one station to another and is called directness. The third attempts to get an overall view of transfer possibilities to travel in the network to appreciate a sense of mobility; it is termed connectivity. Multiple-regression analysis showed a strong relationship between these three indicators and ridership, achieving a goodness of fit (adjusted R² value) of .725. The importance of network design is significant and should be considered in future public transportation projects.