The concept of a link-to-node ratio first came to my attention last year. I was probably just reading something online, without saving the link, but it made such an impression that I told my students about it. I used the published works of
Wesley E. Marshall and
Norman W. Garrick, two civil engineers, to explain the difference between qualitative and quantitative analysis. I drew pictures like the ones at right and below and told students how Marshall, Garrick and their colleague
Daniel Piatkowski (an NSF IGERT Fellow in sustainable urban infrastructure) correlated the connectivity and design of cities with rates of obesity. Their study concluded that straighter streets laid out in a grid housed a smaller number of obese residents, compared with suburbs where residents spent less time walking and more time driving. Makes sense, right? We were discussing "pattern recognition" as a part of the scientific method.
So then goes by 7 months and I had a hard time finding the original article, while my brain still remembered the shapes of the neighborhoods from whatever I had been reading. I haven't been able to retreive the original article by Marshall, Piatkowski, and Garrick (I have requested it via interlibrary loan) but at least I found the article in The Atlantic, which is probably where I originally was reading about this idea in the first place.
The figure below is from another paper by Marshall and Garrick (2010) for which I could get a full text version. It made me think that Glendale, CA is a nice grid, circa 1930. Our neighborhood, at least. Our house was built in 1922. The population of Glendale exploded, increasing 4.5x between 1920 and 1930 due to film and aviation industries. The population of Glendale boomed again in the 1980s with the arrival of many thousands of immigrants, especially from Armenia, the Middle East, Korea, Mexico, and the Philippines.
As I bike around Glendale, I wonder what it would be like to have just moved here. It's recent enough that I remember. I definitely didn't feel safe riding a bicycle, not for fear of getting lost because Glendale is small and there are large landmarks such as the Americana at Brand (centrally-located), the tall buildings of Downtown LA (to the South), and the Verdugo Mountains (to the North). It just feels like the city is disjointed, very few of the bike lanes intersect. It would be hard to ride a loop with continuous bike lanes.
Things have improved since I moved here. Central Ave has a short stretch of bike lane. There are sharrows along Broadway. So I wanted to apply the link-to-node analysis so eloquently described by Jessica Schoner and Jennifer Dill in their respective papers. First, I assembled a list of bicycle infrastructure from Google Maps, the City of Glendale Bicycle Transportation Plan, and Implementation of Bicycle Transportation Plan
Phase I Project.
https://walkbikeglendale.wordpress.com/2013/07/14/monitoring-glendales-bicycle-transportation-plan-implementation/
I printed out the map from Phase 1 Bikeway Improvement
Recommendations because it seemed easiest to draw on. Actually first I tried mapping all the lanes in Google Maps and after I got to 10 layers, it wouldn't let me draw any more. So I did it by hand. I counted up the number of segments, "links," and the termini of each segment as well as intersections between segments, "nodes." I calculated the alpha, beta, eta and gamma indices.
Probably the easiest to understand is the beta index, which is a ratio of links to nodes. Glendale scores a 0.72. Higher beta values constitute a more complex network, whereas lower beta values mean that a cyclist would have to ride in traffic where the network fails to connect points of interest. By this parameter, it seems Glendale is doing OK.
The gamma index is a ratio of observed edges to the theoretical maximum. Glendale scores a 0.25. Higher values of gamma indicate greater internal connectivity and increased redundancy in the network, providing a cyclist with greater choices. I believe Glendale is not doing so well in this area.
The alpha index is the ratio of the number of actual circuits to the maximum number of circuits. If the value is zero, then it indicates no circuits; and if the value is 100 then it indicates complete interconnected network. Glendale scores a -0.13. This is what I expected since it seems our network is very disconnected with no possible circuits.
The eta index measures the average edge length in the network. For Glendale, the average length of segment is 1.18 miles. I guess this is pretty good, but if you cut the city up into segments that don't meet, you could theoretically place a bunch of 1 mile segments all over the city that leave cyclists without a safe way of getting from point A at let's say the West part of South Glendale to point B (maybe the Southeast end of South Glendale or North Glendale). Considering our city covers 30 square miles, I think we can do better (longer average segment length).
Comparing Glendale with the data on 74 US cities (Schoner, 2014), we have 47.4 km of network length. The mean was 300. Our number of nodes was 47 compared with a mean of 202. Our number of links was 34 compared with an average of 191. The mean beta index was 0.81, the mean gamma index was 0.29, and the average alpha index was 0.03.
The thing I thought that was really neat about Schoner's work was that she correlated these beta, alpha, and gamma indices with the number of bicycle commuters per 10,000 commuters. Grouping these factors was the result of exploratory principle component analysis to reduce 18 measures into five factors. What she calls "factor two" describes internal connectivity and complexity of the bicycle infrastructure network. With and without correcting for city size and demograpics, Schoner found that network connectivity (as quantified by alpha, beta, and gamma indices, among other factors) is positively correlated with increased numbers of bicycle commuters.
The bottom line is that
GLENDALE CAN DO BETTER and if we keep pushing for
INCREASED FUNDING FOR BIKING AND WALKING projects in the
San Fernando Valley Council of Governments Mobility Matrix perhaps we can increase our city's profile among bikable cities with interconnected networks of bike lanes.
P.S. Somehow this blog post ended up on a scenic detour to La Cañada Flintridge, originally envisioned in 1912 as a wealthy suburb for the burgeoning city of Pasadena. In the
recent press, La Cañada Flintridge has been accused of ignoring the restrictions on water use, having been found to have the highest per capita water use in Los Angeles County. I bet they also have a sparse neighborhood layout.
P. P. S. We're riding the
Jewel City Gear Grinder ride this weekend to preview the route. The actual ride is on June 7th, 2015 and costs $50 for the 50 miler, $35 for the 35 miler, and $20 for the family ride. Proceeds benefit the Glendale YWCA, ARK Family Center and the City of Glendale Police Activity League (PAL). You can register
here.
References
Dill, Jennifer. "Measuring Network Connectivity for Bicycling and Walking" (
2004) Transportation Research Board (TRB) Annual Meeting. [linked
here]
Marshall, Wesley E. and Garrick, Norman W. "Street Network Types and Road Safety: A Study of 24 California Cities." Urban Design International (
2010) 15, 133–147. [linked
here]
Schoner, Jessica E. "The Missing Link: Bicycle Infrastructure Networks and Ridership in 74 US Cities" Transportation (
2014) Volume 41, Issue 6, pp 1187-1204. [linked
here]
Marshall, Wesley E.; Piatkowski, Daniel P.; Garrick, Norman W. "Community design, street networks, and public health" Journal of Transport & Health (
2014) Volume 1, Issue 4, pp 326-340.
Hamblin, James. "Do We Look Fat in These Suburbs?" The Atlantic. August 13,
2014.
http://www.theatlantic.com/health/archive/2014/08/blame-the-city/375888/
we decided to talk about food, sustainable agricultural practices, and renewable energy. I have long been interested in where food comes from. 
We talked about how plants harness the sun's energy to make sugar, and the sugar content of fruits is why we like to eat them. I wrote the chemical reaction for photosynthesis on the board. Then we talked about things like solar panels, where we use chemistry to capture energy from the sun. We used the map to talk about why certain plants are grown in the desert and other plants are grown in the mountains.
I told the kids that I grow my own food in a garden. They have a student garden at their school, so I gave them a packet of seeds. We talked about renewable and nonrenewable sources of energy. The kids discussed this in groups and then put their conclusions on the board. They knew but didn't write that electricity comes from coal-burning. We talked about how fossil fuels were created when plants and animals died millions of years ago and became trapped under many layers of dirt. Oil, natural gas, and coal are examples of nonrenewable energy. Even using an electric car still indirectly involves combustion of fossil fuel if the electricity is generated in a coal-fired process. 
I showed them a molecular model of capsaicin. I told them that Cayenne peppers are hot because of this molecule. I told them that capsaicin is used in pepper spray (defense) and creams for treating shingles (analgesic). If we had more time, I could have talked about how birds don't "chew" and also don't sense the heat of the hot pepper. The pepper plant relies on birds to disperse its seeds. The capsaicin molecule deters mammals from eating the pepper. Mammals chew and destroy the seeds so the plant has evolved to defend itself. 
