Data Lies

I've received a really important e-mail from LinkedIn today, it said I have 252 contacts I might know and I could add them to grow my network.

First I get a top-notch Math lessons, my small network of 474 (let's call this number n) contacts would grow into a network of 726 (and this one N) contacts!

That's amazing: 474 + 252 = 726

And then, I am presented me with an breath-taking graphical representation of this growth:

Reading the numbers and having a look at the picture, something is a bit... weird... can't you see it?

Well, let's call A to the area of the dark (bigger) circle, measuring its radius R at approximately 72 pixels, 

A = PI * R^2 ~= 16286 pixels.

The radius r = 28.5 of the lighter (smaller) circle, giving an area a of:

a = PI * r^2 ~= 2551 pixels.

The relation between the improved network I'd have and my current one is:

N/n ~= 1.5

whilst the relation between the areas of the two circles is:

A/a = 16286 / 2551 ~= 6.4

Let's review the "Lie Factor" (http://www.infovis-wiki.net/index.php/Lie_Factor)

 Size of effect in Graphic (g) = (16286 - 2551) / 2551 ~= 5.4

Size of effect in data (d) = (726 - 474) / 474 ~= 0.5

Lie Factor = g/d ~= 10.8

To ensure the Integrity of a graphic, its Lie Factor should have a value between 0.95 and 1.05. If the value is less or greater, it indicates a substantial (and often intended) distortion, far beyond minor inaccuracies (e.g. caused by plotting).

4 circles of size 474 fits easily in the 726 circle.

I thought: maybe they've used radii to apply the growth factor...

R/r = 71 / 28.5 ~= 2.5

No. Lie Factor > 2.5.

Now, I don't like being lied to, not even in unimportant facts as a poor infovis. What was the point of this? Imagine other visualisations / info-graphics you might have read...

A' = a*1.5 ~= 3826 pixels 

R' = sqrt(A' / PI) ~= 35 pixels

Seriously, why?