Every day, all over the world, people use Google as their first choice of search engine
What is the deal with Google?
It's well and truly a household name, it's even a verb to Google something Why is it so popular?
Let's go find out.
One of main reasons is their clever mathematical software.
PageRank is a link analysis algorithm, named after Larry Page.
It's used by the Google web search engine that assigns a numerical weighting to each element
of a hyperlinked set of documents,
with the purpose of measuring its relative importance within the set.
Maths is really the core of computer science, so it's vital to what we do here at Google.
So if you come up with the solution or an algorithm to a problem, then maths is the tool
that lets you understand how well that's gonna run, how much time or space it's gonna take
and it's gonna let you then prove whether that's the optimal way of solving
that solution, whether there are better ways.
Or even sometimes if you have a problem, maths can show you is it possible for a computer
to solve that problem at all At the heart of Google software is a system called PageRank.
Which basically gives every site on the Internet a rank between 0 and 1.
So how is this calculated?
Well, the PageRank of your site is determined by the links to your web site.
Each time somebody adds a link to your web site, Google interprets this as a vote for your site.
The more links you have to your site, the more votes you get.
With PageRank what we like to do is think of all the different pages
on the internet as different nodes in the graph.
So if you have Page A and it has a link pointing to Page B then we have those
as two separate nodes with an edge joining them together.
And what we have is when you have all those nodes
and edges together that's what we call in mathematics, a graph.
And once we can understand the internet's connectivity as a graph,
then we can use a whole heap of powerful mathematics to understand it.
Web pages are all linked, they're part of a network.
So an inlink from my page to your page is an endorsement of your page.
The more inlinks your page has, the more important it is.
But if your page has an inlink from a page with many outlinks, then that endorsement
of your page is of lesser value as it is coming from a page that is less discerning.
Ranking anything, really where do you start?
Well one of my jobs is to go through lists of thousands of products and try to identify
which ones are more important than others.
A good place to start is to use the variables as signals of importance, like product price
or how many times a product is viewed.
Then like Google use an algorithm to sort the products from most to least important.
Google PageRank is a probability distribution used to represent the likelihood
that a person randomly clicking on links, will arrive at any particular page.
A probability is expressed as a numeric value between 0 and 1.
Converting this idea into a formula that can be calculated for each
of the 14 billion web pages is an amazing achievement.
And Google guarantees an accuracy between 3 and 7 digits.
Awesome. But let's bring this down to manageable numbers for a second.
Using this small-scale set of 6 people, to represent just 6 web pages.
As with any network, some might know each other I know you.
How do I know you?
I've seen you around.
Yeah you look familiar.
And so have a link.
Some, don't No I don't know you I'm sorry.
Do you work online?
No I don't know you.
Maybe there's just one that they all know of.
Oh yeah. I think I know that guy.
Yes I know him.
Everyone knows him.
Doesn't everyone know Red?
That one then is the most popular and so will get the highest page rank.
In the small example shown here, you can see that P6 has the strongest links.
P5 and P4 link directly to P6.
And there are paths in the graph from P1 and P3 to P6.
Even though we would guess that P6 has the highest Page rank,
it is not at all clear what ranks the other pages would have.
This is where the Google PageRank algorithm comes in.
The first step in calculating the Google PageRank of each page,
is to represent the graph in a table.
The table shows, for example, that there are links from P1 to P2 and to P3.
A neat way to record the results.
The next step is to replace the table by the corresponding 6 by 6 matrix A.
After several manipulations we arrive at the Google page ranking matrix G. Rather
than a tiny 6 by 6 matrix as in our example, the Google matrix G is 14 billion by 14 billion.
The average number of outlinks on a webpage is 10.
This makes it computationally possible for Google to process the matrix multiplication,
to solve the equations and yield a final list of page ranks.
So cool!
It's easy enough finding out who knows who with just six people
But imagine doing this 14 billion times?
That's twice the population of the world.
The thing about Google is that everything we do, we do at a massive scale.
So we are handling billions of pages and billions of emails,
billions of images you name it there's a lot of it, there's a lot of data
and so the maths become critical at every single part
of the product because without it we'd be lost.
Oh great, thanks!