Monday, October 10, 2011

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.


  1. Interesting idea. Yep, I've mostly only been concerned with denser networks as a way to shorten the distance from point to point, but the fact that it can increase the amount of frontage available is an important one.

  2. Nice! It's exciting to see my thesis advisor, Dr. Peponis, recognized for creating a valuable new metric. His corresponding metric, directional reach, highlights another sort of connectivity - long roads accessible from a small number of turns. By comparing the relationship between these different measures, it is possible to describe the sort of logic that generates urban form.

  3. For a good two centuries one of the absolute axioms of urban planning is that cities need open areas or green spaces. Yet everything about the need for density and connectivity seems to contradict that. Is the whole notion of urban parks and greenways a false doctrine?

  4. Thanks for the mention, Charlie. Your list of methods is great, and I also like the "route directness" measure. That's the ratio of straight-line distance to walking distance. The closer the ratio gets to 1, the more direct the route is. The connectivity of a neighborhood could be measured by calculating the route directness from all intersections and cul-de-sacs to all other intersections and cul-de-sacs.

    MIT made a nice plugin for ArcGIS that calculates reach (to buildings or nodes), directness (to buildings or nodes), and other metrics. It's available free from

    In answer to Cambias, a well connected fabric of urban streets can coexist quite nicely with parks and greenways. I suggest this planning principle: As the size of the green space scales up, the distance between streets that traverse the green space becomes greater. Narrow greenways, canals, etc, are crossed more frequently. And there are many beloved neighborhood parks that fit within a city block or a portion of a block.

  5. Cambias, the movement for parks and open spaces developed out of a false notion of public health - that diseases spread because of a lack of access to "light and air". See . Jane Jacobs was reconsidering the usefulness of parks in 1961, when she published The Death and Life of Great American Cities, arguing that the creation of open space was often just code for the destruction of urban spaces.

    Laurence is right - Andres Sevtsuk at MIT just released a "Network Analyst Toolbox" that will calculate a number of network analysis measures. Sevtsuk does not subscribe to Space Syntax, though, and you'll find that his toolkit uses similar names for different measures. His measures are more generic, derived from graph theory rather than Hillier's work.

  6. @Patrick: thanks for the tip about directional reach. I missed that one. Fortunately, I am not being graded on these posts! In any event I'm flattered that one of Dr. Peponis' students has discovered this blog. Is your thesis related to this area of research?

    @Laurence: thanks for the link to that new program. There are a bewildering variety of mapping options out there it seems. Can you (or Patrick) recommend any free software that is capable of computing these elements, or is ArcGIS the best available option?

    @Cambias: this is a complex question. Overall I agree with Laurence that an acknowledgment of the importance of connectivity and density does not undermine the case for urban parks, although it does suggest that certain ways of incorporating them may be more beneficial than others, as Laurence mentions. I would add, though, that some of the supposed benefits of parks only reflect shortcomings of the modern city – if a city is overrun by cars, a park benefits by being a quiet, car-free environment; if a city consists of very wide streets, a park provides human-scaled paths and amenities; if a city lacks street trees or other "urban" greenery, a park satisfies that need. A park ought to be a complement to outstanding urbanism, I think, not a band-aid for poor urban design.

  7. ArcGIS is the industry leader, but once you add in extensions it is staggeringly expensive. So it's really only an option if you have academic or corporate connections. There are free GIS programs available, but they look challenging at best (for instance,

    The easiest option is the new Street Smart Walk Score ( You input an address, and it shows the average block length and the intersection density for the area within a 15 minute walk. The Walk Score map is missing many routes such as alleys, but Walk Score uses OpenStreetMap, which you can edit.

    If anyone has other suggestions for free or low cost options, those would be great to learn about.

  8. Yes, my thesis uses several measures of metric and directional reach. I am comparing the reach values to the distribution of commercial space in Atlanta. It is still a work in progress, but I hope to have it done in a month or so.

    We use a command-line utility called Spatialist Lines to calculate reach, and I'd be happy to sent it to you if you like. It operates on shapefiles though, so you would still need access to a GIS package.

  9. This is a great way of explaining the connectivity issue, and I love the visuals. I am reminded of one of the coolest towns I've been to, Guanajuato, Mexico, which probably was built in a similar style to Malaga.

    One issue I hope you'll get to, though, in the next post is navigability. I have a terrible, terrible sense of direction. I appreciate the beauty of cities like Malaga, that stray from the rigid grid pattern, but if I were to step off of a train there I would be totally lost. Grid systems can certainly be improved with shorter blocks, narrower streets, and alleys, but is there always a correlation between connectivity and a non-grid layout?

  10. Emily: that's a great question, and I will try to address it in the next post, hopefully coming soon. I have a feeling Patrick might have some thoughts on this also.

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  12. Hi all, regarding software, i would recomend QuantumGIS (, since it is open source, it as many of the capabilities of ArcGIS, it functions as a GUI for Grass and other raster/vector GIS processing software, and already has at least one space syntax plugin (check the plugins in the qgis site). If you have access to ArcGIS you could use axwoman, from Prof. Bin Jiang ( He and Xintao Liu have worked out a way of using openstreetmap open data as a base for creating automatically axial lines (