3. Analysis: what the results mean

Before we start, you have prepared your network, haven’t you? If you haven’t, then go back to Network Preparation. It’s very important.

This section provides an informal introduction to the outputs of sDNA Integral Analysis. Although it focuses or urban networks, the discussion is relevant to all domains of network analysis. A picture speaks a thousand words, so let’s begin with one.

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Figure 1: Cardiff link density, 1km radius. Basemap (c) OpenStreetMap contributors

3.2. Betweenness

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Figure 3: Cardiff Angular Betweenness, Radius 10km. Basemap (c) OpenStreetMap contributors

The flow model inherent in sDNA is based on Betweenness. Figure 3 shows an example. Note this is link-weighted, so the result you see is based on the shape of the network alone.

Betweenness analysis assumes your network is populated with entities that go from everywhere to everywhere else, subject to a maximum trip distance determined by the radius. We assume these entities travel via the shortest possible path – and we call such a path a geodesic. But how we define “shortest” may vary. We call the definition of distance a metric; currently sDNA supports

  • Euclidean metrics, taking the shortest physical distance possible
  • angular metrics, which minimize the amount of turning both on links and at junctions
  • custom metrics based on user data
  • hybrid metrics which are user programmable (requires sDNA+)
  • specialist metrics for cyclists, vehicles and pedestrians (requires sDNA+)

As a first approach to most urban network problems, we really like using angular metrics. Pedestrians, unless they know an area very well, will tend to follow the shortest angular paths, because they are easier to remember (“second on the right then straight on ‘till morning” – Peter Pan would probably have got lost had he tried to take a short cut requiring more complex directions). Drivers of vehicles also tend to follow angular geodesics, but for a different reason – straight roads through a city tend to be faster, on average. So we have set the default metric in sDNA to be angular.

Take care, however, to set the radius for your intended purpose! A realistic indicator of pedestrian flow might be Betweenness Ang R800, while a realistic indicator of vehicle flow might be Betweenness Ang R2000, or higher. But fish, for example, probably don’t care much about going around corners in rivers, so Euclidean analysis might be more appropriate. Pedestrians commuting to and from work tend to follow Euclidean geodesics too, because they know all the short cuts.

Note that in betweenness analysis, we are usually looking at an intermediate link in a trip, not the origin or destination. This means that the radius has a subtly different meaning: a calculation of betweenness R500 does not involve all possible trips within 500m of the link you are observing, but involves all possible trips that pass through the link you are measuring with a maximum length of 500m (almost: see Geodesic for more details).

A final question in betweenness analysis is what weight to assign to each geodesic. The simplest answer is to assign a weight of 1 to every pair of links. As the density of jobs and homes is strongly related to the density of network links, betweenness weighted in this manner usually correlates well with traffic flows. But what if network length is important to you? Let’s say you want to assume longer streets act as origins and destinations for more people, or you’re analyzing rivers, etc. Or maybe you have custom weights - census data for example, or building entrances. In this case we assume the number of entities making the trip is proportional both to the weight of the origin and the weight of the destination, so we multiply the origin weight and destination weight together to compute the betweenness weight.

Interestingly though, such flows scale with the square of the number of links in the network, implying that more dense areas contain more activity per link - in other words, an opportunity model. (To a physicist, there is a problem with the units: Betweenness is measures in units of weight squared, not weight). If this is not desirable then instead use a Two Phase Betweenness model. These assume each origin has a fixed amount of weight it can add to betweenness – in the case of cities, a fixed quantity of journeys that the people living there will realistically make. This fixed quantity is then divided proportionately among the destination weights accessible from that origin for the current radius; this can be described as a generation-distribution model.

Complementing Two Phase Betweenness is Two Phase Destination – the quantity of visits each destination gets under the two phase model. In the normal betweenness model, each destination will be visited by everything within radius x, so this measure would be equivalent to Weight. But in a two phase model, destinations must compete with other destinations for the attention of origins, and TPDestination measures the total flow to the destination taking account of this competition. A real world example would be the case of high street shops - with small destination weight - trying to compete with an out-of-town retail park - with large destination weight. Both may have lots of population in their catchment (which will show up in the Links Rx measure) but the town centre loses out to the new development (which shows up in the TPDestination Rx measure).

That said, all the forms of betweenness tend to correlate quite well with actual flows of pedestrians, vehicles etc.

3.3. Closeness

Closeness, like betweenness, is a form of network centrality. It matches commonly held notions of accessibility.

Mean Distance is perhaps one of the most common closeness measures in the literature. It measures the difficulty, on average, of navigating to all possible destinations in radius x from each link. Technically then it’s a form of farness not closeness: this only means that big numbers mean “far” instead of “close”.

“Difficulty” is defined in terms of the same metric used for Betweenness: Euclidean, angular, custom, hybrid, and so on. sDNA names its closeness outputs Mean Angular Distance (MAD), Mean Euclidean Distance (MED), Mean Custom Distance (MCD), etc.

Note that the “mean” of mean distance is weighted by the weight of destinations.

3.4. Other measures

sDNA produces numerous other output measures, for a full description refer to Analysis: full specification.

sDNA+ can also display the geometries of geodesics, network radii and convex hulls used in the analysis, as well as producing accessibility maps for specific origins and destinations.

3.5. Summary of measures

Measure Abbreviations Description
Closeness (mean distance)/Farness MAD, MED, MCD, MHD Inverse of closeness, accessibility
Mean Geodesic Length MGLA, MGLE, MGLC, MGLH As closeness but always output in units of length even for non-Euclidean geodesics
Network Quantity Penalized by Distance NQPDA, NQPDE, NQPDC, NQPDH Sum of network quantity over distance
Betweenness BtA, BtE, BtC, BtH Flow model, through-movement
Two Phase Betweenness TPBtA, TPBtE, TPBtC, TPBtH Generation-distribution flow model
Two Phase Destination TPDA, TPDE, TPDC, TPDH Floating catchment, competitive accessibility
Mean Crow Flight MCF Mean distance to destinations as crow flies
Diversion Ratio DivA, DivE, DivC, DivH Mean ratio of geodesic length to crow flight distance
Convex Hull Area HullA Area of convex hull of radius
Convex Hull Perimeter HullP Perimiter of convex hull of radius
Convex Hull Max Radius HullR Furthest extent of convex hull; crow flight distance for most efficient route
Convex Hull Bearing HullB Bearing of furthest extent / most efficient route
Convex Hull Shape Index HullSI Describes shape of hull; ranges from 1 for circle to infinity for straight line
Links Lnk Links in radius
Length Len Length in radius
Weight Wt Weight in radius
Angular Distance AngD Angularity in radius
Junctions Jnc Junctions in radius
Connectivity Conn Connectivity in radius
Line Length LLen Length of individual polyline
Line Connectivity LConn Connectivity of individual polyline
Line Angular Curvature LAC Angularity of individual polyline
Line Hybrid Metric HMf, HMb Hybrid metric of individual polyline
Line Sinuosity LSin Diversion ratio for individual polyline
Line Bearing LBear Bearing of individual polyline
Link Fraction LFrac Fraction of link represented by polyline

3.6. Calibration

sDNA produces network statistics that correlate to real phenomena such as traffic flows or land prices, but if you are interested in predicting these phenomena, you will need to know how to convert sDNA outputs into a prediction. This is done by regression analysis, a huge topic with which some users of sDNA will already be familiar, but others won’t.

sDNA provides two tools to help with this process, Learn and Predict. Learn takes a sample of real data and creates a model linking it with the output of sDNA. Predict takes a model created by Learn and applies it to new areas where data is not available, based on an sDNA analysis of those areas.

Of course, it is also possible to use any third party regresion software of your choice to perform these tasks.