Graphs: uses and abuses

Given that a third of the human brain is devoted solely to making sense of what we see, it’s both unsurprising and surprising that graphs frequently feature when we want to present information...

It's unsurprising because numbers can hide a multitude, so displaying data graphically can make patterns much easier spot. But what's surprising is that, despite maths going back millennia, it actually took until the 1700s for someone to invent graphs in the first place.

That person was the Swiss mathematician Leonhard Euler, who famously solved a problem called the Bridges of Konigsberg puzzle. The Prussian town of Konigsberg, now Kaliningrad, was carved up by the River Pregel into 4 blocks of land linked by 7 bridges. It’s said that locals out for a stroll would try to take a route that crossed every bridge but only once. No one knew if it was possible.

Euler’s insight was to reduce the problem to a simple graph: the land masses became blobs and the bridges were lines connecting them. Presented like this, the solution was easy to prove, and with it the world’s first network diagram, and the science of the graph, were born.

These days graphs are everywhere. We use them to show how values compare: does my county have more coronavirus cases than the one next door? How data are distributed: what are the blood oxygen levels of Covid-19 patients who do or don’t need intensive care? How data are composed: what proportion of Covid cases affect different age groups? And a heat map showing where coronavirus cases are changing most rapidly across the country is also a graph.

In all these cases, graphs transform detailed patterns and relationships between numbers into a simpler visual stimulus that makes it easier for the brain to comprehend quickly. But, as the phrase popularised by Mark Twain goes, there are “lies, damn lies and statistics,” and the power of the graph to hijack our attention and short-circuit our understanding is often abused too.

Watch out for the crafty use of scales: tiny differences can be grossly exaggerated to emphasise a political point, or massive losses shrunk into invisibility to make an inconvenient truth disappear. Moreover, apples can end up being compared with oranges because graphs don’t tell you where the data they represent came from.

At the moment, UK cases of Covid-19 test results are being displayed on the same graph alongside data from 6 months ago, giving the impression that there were more cases of Covid-19 in the country in October than there were in March. What the graph doesn’t tell you is that, back then, only a few thousand tests were being carried out each day compared with half a million today, so the pick-up rate is now far higher.

The best graphs are the simplest graphs that don’t seek to deceive, contain only the crucial pieces of information, have a clear scale and use the fewest colours to make the most important trends apparent.

And for those of you still pondering the Konigsberg puzzle? Euler’s graph proved it’s impossible...