Measuring Connectivity, part I

The subject of street connectivity is one which gets to the heart of what is and is not good urbanism.  It formed the basis for one of Jane Jacobs' most memorable discussions in The Death and Life of Great American Cities when she singled out New York's 800-foot blocks for particular criticism.  Two decades later, Professor Bill Hillier developed the analytical method for spatial patterns known as space syntax, an approach which promised an objective means of ascertaining the intelligibility and effectiveness of  street networks.  The area has become a fruitful field of study, while an abundance of free software tools have put spatial network analysis within the reach of the humble blogger.

What is connectivity, then, and why is it so important?  It is not a secret that the purpose served by streets is, among other things, to provide a public means of accessing the built environment.  It is just as evident that a public way adds value to the adjacent land.  A city therefore exists in tension between the value of land for buildings, which encourages a maximization of the built footprint, and the value added by streets, which by their nature diminish that same footprint.

The value conferred by the streets themselves, however, depends upon their accessibility to the public, not merely in a legal sense, but in terms of proximity and navigability.  A shop at the end of a long, dead-end street benefits from that street far less than the shop at an intersection benefits from its adjacent streets.  In general, then, a city as a whole will have an economic incentive to maximize continuous streets and minimize cul-de-sacs, except in rare cases.  Connectivity, in this sense, describes to the extent to which various points within a given area are linked by the street network, just as density can describe the intensity of the built environment.

Academics and planners, in the field of space syntax and outside it, have developed numerous different approaches aimed at measuring this elusive quality.  Among these are:

• Intersection density (the classic measure often used to contrast between gridded patterns and late 20th century suburbia).
• Link-node ratio.
• Connected node ratio.
• Distance between origins and destinations.
• Average block sizes.
• Block density.
• Block face lengths.
• Street density (street area).
• Metric and directional "reach."

(For a summary of many of these, see here).

The newest of these, metric reach, is a concept introduced by Georgia Tech's John Peponis just a few years ago.  The concept is defined as:

"[T]he aggregate street length that is accessible from the mid-point of each road segment within a metric radius of actual movement.  ... Distances are measured along street center lines ... Reach, therefore, is a measure of street density. Implicitly, it is a measure of urban potential: the greater the average [reach value] of an area the greater the interface between the public streets and private properties, the greater the the likely number of properties that are within range, the greater the likely number of potential destinations or land uses." (Peponis et al. 2007).

To illustrate the method, consider the central areas of two cities of roughly equal population: Omaha, Nebraska (at left, of course), and Malaga, Spain.  A single point is selected from which are drawn all possible routes that could be covered in a 900 foot walk:

As it turns out, a person in Omaha can, within 900 feet, access 13,800 linear feet of block fronts (several of which happen to consist of parking lots), while the pedestrian in Malaga, in the same walking range, can access just under 25,000 feet.  And despite this, Malaga has a considerably higher ratio of built area to street area, thanks to streets which are, overall, much narrower than in Omaha.  Malaga obtains both higher density and connectivity, at least by this single data point and using this particular method. 

What predictive power does this measure have for pedestrian and economic activity? I'll discuss that in the next post.

Related reading: Laurence Aurbach has a fantastic series on connectivity which I highly recommend.