Visualising PageRank and its PR Bar graph using the Google Toolbar:

Google does not calculate PageRank for a single web site. It calculates the PageRank for every page on the whole web (or rather its indexed database) in one sitting this is what is happening during what is commonly referred to as the Google Dance. This takes place about monthly.

If the whole web consisted of 1,000,000 interlinked pages and a surfer started clicking on links in a random manner then for a web page having a PageRank of say 1,000 that surfer in 1,000,000 surfing starts would probably hit the web page with a PageRank of 1,000, a thousand times on average (ie the PageRank).

For a site with a PageRank of only 100 the same surfer would hit it ten times less frequently. This kind of thinking puts into perspective the importance of Yahoo with hundreds of thousands of links pointing to it. This was the intuitive thinking behind Brin and Pages theory and PageRank algorithm.

The Google tool bar which was discussed earlier is shown below to refresh your memory.

Note the green horizontal bar called PageRank. This bar is a representation of actual PageRank. The actual scale is not known outside Google but it is known to be logarithmic in nature. This means using the log base of 10 we are generally familiar with that a PageRank of exactly 4 on the bar chart is 10 times bigger than exactly 3 on the same bar chart. If the log base was 5 as some believe then PageRank 4 would be 5 times bigger than PageRank 3.

PageRank 2 could have an actual numerical value of say 100, or it may be 1,000, only Google knows.

PageRank mathematics simplified

In calculating PageRank Google needs to know the number of links from every page on the whole of its indexed database. It also needs to know where each link goes to enough to prevent you sleeping at night

This table shown next is exactly what Google does to determine the number of links from every page. For the sake of simplicity I have assumed the whole matrix of web pages is only a total of 8 (refer actual table in my book)

PageA PageB PageC PageD PageW PageX PageY PageZ Total of links

PageW 1 1 1 0 0 1 1 1 6

PageX 2 1 0 1 0 0 1 1 6

PageY 1 1 1 1 1 0 1 0 6

PageZ 0 1 1 1 0 1 0 1 5

PageA 1 1 0 0 1 0 0 0 3

PageB 0 0 0 1 2 0 0 1 4

PageC 1 1 1 0 1 1 1 1 7

PageD 0 2 1 0 0 0 1 1 5

The total column represented by the red numbers represents the total number of links from say PageW (vertical column) to other pages (on horizontal row) on the whole database. In This case PageW has 6 links out. The importance of this number is that in calculating PageRank for every page on the whole web Google would calculate (by reiteration) the PageRank of PageW, divide it by 6 and add 1/6th to PageA and PageB and PageC and PageX and PageY and PageZ ie all those pages PageW is actually linking to.

Even though the above shows that in some cases there are 2 links from the same page to another page only one of these links is probably calculated.

The strength of Google compared to other search engines is that it can do all these vast numbers of link interpretations and then do massive amounts of reiterative calculations at low cost by virtue of the mathematical PageRank algorithm it developed and then patented.

Now take a look at the next table with exactly the same numbers.

What do you think the totals in blue represent?

PageA PageB PageC PageD PageW PageX PageY PageZ Total of links

PageW 1 1 1 0 0 1 1 1 6

PageX 2 1 0 1 0 0 1 1 6

PageY 1 1 1 1 1 0 1 0 6

PageZ 0 1 1 1 0 1 0 1 5

PageA 1 1 0 0 1 0 0 0 3

PageB 0 0 0 1 2 0 0 1 4

PageC 1 1 1 0 1 1 1 1 7

PageD 0 2 1 0 0 0 1 1 5

Total 6 8 5 4 5 3 5 6

These totals are representations of relevance and/or high citation. Page B has the highest number of links to it and is thus probably highly relevant and would probably have the highest PageRank.

You can draw this table for every one of your own web sites to attempt to get greater visual understanding of relative importance of your pages and where you can increase/decrease links to re-allocate PageRank within your own web site.

PageRank continued