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The rest of my talk at Que Du Web 2017 in Deauville.
In this third part, we get into something more concrete for SEOs, with the PageRank algorithm: why it’s often misunderstood (and therefore misused), and how to approach it properly so you really understand how PR flows through your site.
(See the overview of the talk with all the episodes)
The matching slides:
The transcript
The brain is a graph…
So last week we saw that graphs are useful as a visualization for passing on information, and I left you with a question about very complex graphs, like the brain, for example. Is there a complexity threshold beyond which graphs become useless?
Actually, not at all, and to explain why, I need to introduce you to Leonhard Euler.
He was an astronomer, an engineer, and incidentally a mathematician.
The people of the small town of Königsberg came to him with a puzzle about their Sunday walks over the town’s bridges.
Their goal was to walk through the town crossing each bridge once and only once.
At first, he told them to take a hike, quite literally.
But it kept nagging at him, and he realized that the problem could be solved neither by calculation nor by geometry.
It took him a year of work, and he invented a new branch of mathematics:
Graph theory.
So we already had the graph as a representation, but since Euler, the graph has become an extremely powerful mathematical object, with its share of properties, algorithms, and so on…
And that’s what the web as we know it today is built on.
To get back to a concrete example, here’s an example of what the mathematical object makes possible:
Here we have a graph representing a website, which may be too complex to analyze as it is.
The theory lets us reduce it to a tree, while keeping carefully chosen properties.
We then get something much clearer, whose structure we can appreciate better and in which we can isolate flaws (here, for example, big pagination and duplicate content issues).
We’ll now move on to SEO applications of this theory, and an algorithm you can’t get around:
PageRank.
Named after Larry Page, one of Google’s founders.
It’s an algorithm designed to gauge the importance of a site by factoring in external signals, “votes”. This algorithm is truly at the heart of Google, and it’s both its greatest strength and its greatest weakness.
Very often, among SEOs, this algorithm is misinterpreted.
Why?
The first approach, the historical one from the patent, is the random surfer. A surfer who wanders from page to page following the links, the way the people of Königsberg followed the bridges…
But that gives you a probability of presence, and that scares everybody (well, almost).
The other approach is diffusion: it’s an iterative method, which gives exactly the same result: the underlying mathematical object is the same.
And the usual problem is reasoning with the second paradigm, but without grasping the iterative side, and then you get it wrong…
Donald Knuth tells us
“An algorithm must be seen to be believed”
And he’s absolutely right, because if you don’t know what the algorithm does, well… you’re toast.
To see and understand these two sides of PageRank, you can use NetLogo.
It’s a desktop tool that @ThomasCubel pointed me to.
You can simulate and step through both algorithms, tweak the parameters, and believe it or not, you learn a whole lot from it.
For example here, in the diffusion method, we started with an identical weight on every node, and we took one step. Each node has “diffused” its PageRank to the nodes it’s linked to.
That’s often how SEOs reason: a link “pushes”.
Except that’s wrong, because it forgets the iterations, which can change everything.
(Which is the case here, in fact)
And once you’ve really understood how PR flows, you see things that are far from intuitive.
For example, linking to a page doesn’t necessarily raise the target page’s PR.
You can see it in this first example: I want to push this page by linking to it from a strong page, a big reservoir of surfers. But the surfers who land on this page have only one choice: to leave and go around in circles on the 3 pages that follow. We wanted to raise this page’s PR, and we raised the PR of the next 3 pages instead…
Second counter-intuitive effect of PR: it only passes on at a (very) local scale.
You can see it in the next case, where we’d like to “push” the page at the end of the chain through a cascade effect.
But what do the surfers do? At each intermediate page, they have a 1 in 5 chance of going somewhere else rather than straight on. 5x5x5, 125… a 1 in 125 chance of reaching the page you want.
And again, this is a case of very light linking. Imagine a site with denser linking, for example with 100 links per page: 100x100x100: 1 million. How much juice reaches the final page? None.
If you’re thinking linking density, mega menus, alarm bells should be ringing!
The right paradigm, then, I’m going to call “Goldiloops”.
For the loops and the golden rule, but also in memory of the tale “Goldilocks and the Three Bears”.
What matters is loops, and short loops.
Not too much, not too little. Linking that’s neither too dense nor too sparse, a site that’s neither too deep nor too shallow.
Here’s an example of an interactive visualization on cocon.se, showing how a deep page on the site gains internal PageRank thanks to loops with other pages, including the menu pages.
If you think in terms of the random surfer, it makes sense: every path the surfer takes from this page lets them come back to the page: it increases their probability of being on this page.
It’s quick, but I’m trying to give you an overview rather than focusing on one particular technical point.
So the general methodology when working with graphs (or other mathematical objects) goes like this:
You start from a “real” object that you convert into a graph, a mathematical object.
For a website, the parallel between the two is still simple. Pages are nodes, links between pages are edges.
Once you have the graph, on the one hand you can visualize it, so get a view of your site, but you can also run mathematical computations, and this kind of computation for instance, going from a complex graph to a simpler tree that will clarify the situation while keeping certain properties, is something of real practical value that you can still visualize, the tree itself, which you can map back onto the real object, the site, and so observe certain properties directly.
This back-and-forth, simple here, between the real object and the mathematical object lets us understand a huge amount.
There are cases where it’s a little less easy.
Site <=> Graph, easy.
In Euler’s historical case of the bridges of Königsberg, with the different bridges being the links between the nodes (the riverbanks), the parallel is still easy to make.
But we can go even further, and next week I’ll take you through an algorithm that is much further removed from the mathematical object than that, and that has concrete applications, especially for the web and SEO.
So there you go, run your own tests with NetLogo, and next week I hope to show you something concrete that will be useful in your SEO work.