How visualising networks broke my browser

Networks: aren’t they great? The sexiest modelling paradigm around at the moment and there are no shortage of social science researchers itching to jump on the bandwagon.

Never one to drag my heels, I blogged last week about the attempts by me and my colleagues to bring network science into Economics, and included a fancy graphic to demonstrate how visualising networks can look pretty, and potentially be informative about systems with complex interconnections.

An imagined network of three countries, Red, Blue and Green, using three products, A, B and C internally as intermediate inputs to the production process, and also trading these products with one another.
An imagined network of three countries, Red, Blue and Green, using three products, A, B and C internally as intermediate inputs to the production process, and also trading these products with one another.

But the image I included was static, prepared in a piece of open source network analysis software called Gephi (it’s one of those pieces of software that everybody hates, everybody uses, but no one understands). The natural extension to this is an interactive network diagram. Imagine if we could play with the network shown in that picture. How cool would it be to be able to drag the nodes around to see how the network responds?

Well, there is a way; and, in fact, it’s been done many times before. This cool-looking interactive visualisation is by web-visualisation guru Mike Bostock. The guy brings together insane technical skillz (he seems single-handedly to have written the popular javascript visualisation library d3) with an eye for beautiful design that leads to some of the most breath-taking infographics on the web.

His network visualisation uses something called a force-directed graph in which physics equations are used to determine the behaviour of a network. The nodes (drawn as circles) repel each other like charged particles, and the links between the circles act like springs, pulling the nodes back together. This leads to a balanced state where the nodes are as far apart from each other as they can be, under the constraint that they’re attached together with springs of varying strength.

The network shown in Mike Bostock’s example is pretty simple, but it struck me as a great way to visualise my network of networks. Here’s an example. This is Great Britain’s economy in 2009. Each circle is a sector of the economy, and a link between two sectors shows the extent to which one sector sold goods to the other in that year. For simplicity, most of the smaller links have been filtered out (otherwise, the whole thing is a tangled mess!)

This is great: the sectors are circles, with the bigger circles being the bigger sectors overall, and the connections between the circles being the value of the goods sold from one sector to another. The thicker the line, the more goods were sold.

But there’s a key piece of information missing from this way of viewing the network: the flows between sectors have direction, that is to say, it matters that sector A sold £100 worth of stuff to sector B, rather than the other way around. So how to visualise the network in a way that emphasises the directionality of the links as well as the size?

We could try putting arrows on the ends of the links, right? Mike Bostock has thought of this already of course, and has a simple example here. But the problem is that the circles in his example are a fixed size. If the circles were bigger, the arrows would get hidden underneath them. How to place the arrows when the circles are all different sizes and the line connecting them is ‘bendy’ is an ‘unpleasant’ maths problem.

How to place an arrow when circle sizes differ

I wrestled with putting arrows on the lines for a while before abandoning the project altogether. Then, after some skillful Googling (as vital to the 21st century citizen as reading and writing was to citizens of previous centuries) I came across this from Mike Bostock’s website:

Making a gradient follow a path

With this idea, I could make each end of the links a different colour with, say, red being the seller’s end, and green being the buyer’s end. On a very small subset of my UK 2009 economy network, things seem to work pretty well:

but the computational overhead is massive. Each line in this network is really a group of around 30 little pieces of line, each with its own colour, creating the effect of a smooth transition from green to red. That means that the browser has to work much harder than it otherwise would have to. This approaches scales very poorly. Here’s a slightly more filled out network (these videos are real-time captures of my browser’s output):

Although the network is still a tiny fraction of the complete picture, things are already starting to slow down. Finally, just to really push things to the limit, here’s the network as shown in the very first video in this post. As you can see, although the resulting network looks “pretty cool” (for which read, mind-bogglingly complex) my browser has basically ceased to function. It takes around ten seconds to process each frame of the animation.

So it looks like the colouring of the links is not workable. Watch this space for more updates as I try different methods for showing a big network with directed links.