# Transportation Geography and Network Science/Circuity

Euclidean Distance
Network Distance

Circuity is the ratio of network to Euclidean distance (its reciprocal is Directness)

The presence of a transportation system (including networks and modes) dissuades people from traveling to their destinations in a straight line by providing the opportunity to move faster if more circuitously; while buildings, and other infrastructure (including transportation networks when they act as barriers), and features of nature such as rivers and mountains may constrain the direction of movement.

Distances in transportation research can be measured using geographic information systems (GIS) in three forms: Euclidean distance, network distance, and Manhattan distance. Manhattan distance is not commonly used in transportation research since it is generally meaningful only on a grid system, which holds strictly in few urban contexts. Euclidean distance is the airline distance measured between origins and destinations "as the crow flies", while the network distance, which is a more realistic representation of movements between origins and destinations, is the distance between origins and destinations measured along a transportation network, usually using the shortest path (Miller 2001), these are shown in the figures.

## Evidence

Love and Morris (1979) estimate road distance between two points using analytic models primarily for facilities location problems. Newell (1980) indicated that network distance measured for a randomly selected set of points in an urban environment is about 1.2 times the Euclidean distance. Other research O'Sullivan (1996) finds circuity factors of 1.21 to 1.23 at various transit station catchment areas. The measure has also been used at the national level Ballou (2002), and for pedestrian and bicycle travel (dubbed pedestrian route directness) (Dill 2003), with much higher values than observed for automobile travel. The measure has also been considered by Wolf (2004) using GPS traces of actual travelers route selections, finding that many actual routes experience much higher circuity than might be expected. Samaniego and Moses (2008) find that road networks are built as if traffic is completely decentralized, while travel itself remains mixed between centrality (all destinations in a central business district) and decentralization (trips go to the nearest destination), perhaps explaining some of the observed circuity. Selection of any random pair of points in an urban environment and measuring circuity (the ratio of network to Euclidean distances) may lead to a different answer than the circuity experienced from an actual selection of an origin and destination by locator-travelers.

A question that arises is whether the differences between Euclidean distance and network distance are small and constant. Levinson and El-Geneidy (2009) test that proposition, positing that this assumption only holds when variation in the network is minor and when self-selection is not present. The issue of self-selection has largely been neglected in analysis of network circuity. While it is commonly understood that residents choose homes considering attributes of accessibility to work, shopping, schools, amenities, quality of neighborhood life, availability of public service, quality of the house (number of bedrooms, bathrooms, etc.) and costs of living, the implications of this for measurement of circuity have not previously been noted in the literature. An analysis of circuity bears on the question of home-work location.

Levinson and El-Geneidy (2009) show that circuity measured through randomly selected origins and destinations exceeds circuity measured from actual home-work pairs. Workers tend to choose commutes with lower circuity, applying intelligence to their home location decisions compared to their work. The authors posit this is because locators wish to achieve the largest residential lot for the shortest commute time, all else equal.

## References

Based in part on Levinson, David and Ahmed El-Geneidy (2009) "The minimum circuity frontier and the journey to work" Regional Science and Urban Economics Volume 39, Issue 6, November 2009, Pages 732-738. doi:10.1016/j.regsciurbeco.2009.07.003

Ballou, R., Rahardja, H. and Sakai, N. (2002), “Selected country circuity factors for road travel distance estimation”, Transportation Research Part A , Vol. 36(9), Elsevier, pp. 843– 848.

Dill, J. (2003), “Measuring network connectivity for bicycling and walking”, Unpublished paper presented at Joint Congress of ACSP-AESOP, Leuven, Belgium, July .

Love, R. and Morris, J. (1979), “Mathematical models of road travel distances”, Management Science , Institute of Management Sciences, pp. 130–139.

Miller, H. and Shaw, S. (2001), Geographic information systems for transportation: principles and applications, Oxford University Press, USA.

Newell, G. (1980), Traffic flow on transportation networks, MIT Press Cambridge, Mass. O’Sullivan, S. and Morrall, J. (1996), “Walking distances to and from light-rail transit stations”, Transportation Research Record , Vol. 1538, Trans Res Board, pp. 19–26.

Samaniego, H. and Moses, M. (2008), “Cities as organisms: Allometric scaling of urban road networks”, Journal of Transport and Land Use , Vol. 1(1), pp. 21–39.

Wolf, J., Schoenfelder, S., Samaga, U., Oliveira, M. and Axhausen, K. (2004), “Eighty Weeks of Global Positioning System Traces: Approaches to Enriching Trip Information”, Trans- portation Research Record: Journal of the Transportation Research Board , Vol. 1870, Trans Res Board, pp. 46–54.