Google PageRank Formula: Changes Over Time

To more fully understand how Google calculates and assigns PageRank, it’s necessary to consider the changes made since the inception of the formula. Wayne Hurlbert sheds light on the Topic-Sensitive PageRank calculation method.

Google PageRank is a fundamental building block of the Google algorithm. While the relative weight and importance of PageRank is debated by search engine optimization (SEO) professionals, there is little doubt that Google considers the measure to be important. From the very beginning of Google’s rise to the dominant search engine, its search algorithm has placed varying levels of emphasis on PageRank.

Started as a fairly simple and elegant formula, PageRank determination has undergone a number of changes over time. Exactly what those changes entail has been a source of debate within the SEO community. The generally agreed upon PageRank calculation involves more factors than simply examining the sending page’s PageRank level and the number of links on the page. To more fully understand how Google calculates and assigns PageRank, it’s necessary to consider the changes made since the inception of the formula.

Search engine optimization experts believe that many more factors have been added to the Google PageRank calculation formula. While many of the potential additions to the formula are speculative, there is some evidence as to their being included in the consideration. They include sending and receiving page themes, and sending and receiving page topics. In fact, on and off page topic consideration has opened up an entirely new SEO field called Topic Sensitive PageRank (TSPR).

Search engine optimization experts who are searching for ways to increase their Google PageRank have many more factors to consider than previously thought. Because Google has obviously changed their PageRank formula, we need to examine the many possible factors used in that new calculation, including Topic Sensitive PageRank.

Understanding the many factors considered in calculating Google PageRank will enable you to raise the PageRank levels for all of your web pages.

PageRank was originally designed as a form of voting system. A link to a page was considered a vote for that page. Higher PageRank pages were viewed by Google as being more important. Their votes were given more value by Google. In some cases, much more value.

Adding incoming links to your web pages will add PageRank. Every inbound link adds some PageRank, regardless of its own level. PageRank flows from one page to another, adding to its store of importance. That simple idea has undergone some alteration over time, as we shall see.

Not all incoming links provide the same inflow of value. It may take many PR2 incoming links to increase your targeted page to PR5. On the other hand, it might only take one PR6 page to give you the same result.

Google has published their original PR calculation formula:

PR(A) = (1-d) + d(PR(t1)/C(t1) + … + PR(tn)/C(tn))

While we are not certain if this formula is still the one used by Google, it is probably at least very similar.

In the formula, PR(A) is the PageRank of the page = (1- d) where d is a damping factor considered to be about 0.85 + d(PR(t1) where t1 is the PR of the incoming link page + …+ PR (tn) is the Page Rank of all of the linking pages. Each page is divided by C, which is the number of outgoing links from each page.

Note that the PR flow from a page is divided equally between all of the links on the page. If a page has one outgoing link, that receiving page gets the entire flow. If there are ten links on the page, the PR flow is divided ten ways, lessened by the 0.85 damping factor.

Simply put the formula is this:

PR(A) = .15 + .85 * the PR share of every incoming link page.

Based on the formula, the more incoming links from higher PR pages the better. On the other hand, fewer outgoing links from the sending page, the better too. You get less PR if it’s divided among more outgoing links. Everyone gets their share of the PR pie. Your piece simply becomes smaller if there are more mouths to feed!

You can theoretically gain more total PR from a PR4 page, where you are the only recipient, than from a PR8 page divided 100 ways.

The bottom line is to add, within the context of an overall linking program, as many incoming links as you can. They all add PR to varying degrees.

The original PageRank formula may still serve as a general guideline for providing an estimate of the potential PageRank from a donor page. The originally published formula no longer tells the entire story. It has only served as a very rough estimate for quite some time. One thing to keep in mind, however, is that all discussions of the Google PageRank formula are purely speculative. No one knows the precise calculations involved, and Google isn’t talking.

Since the original PageRank formula was published, Google has made some important changes in its method of PageRank calculation. In the past, the PageRank of any given web page was important in its own right. Little emphasis was placed on the relevant relationship between the sending and recipient pages. With the addition of a number of possible extra dampers, along with Topic Sensitive PageRank, simply having an incoming link from a page doesn’t ensure the full transfer of PageRank.

It is becoming apparent to most Google watchers that all incoming links do not provide equal levels of PageRank transfer. By that I mean you don’t appear to receive as much PageRank flow from a page that is not about a similar topic as your receiving page. On the other hand, a page sharing the same or at least complementary topics will receive a greater amount of PageRank inflow.

The old idea of any PageRank will transfer to your page simply doesn’t appear to be the case any longer. While all incoming links transfer some degree of PageRank, as per the original formula, there are now additional layers of calculations being made regarding the inflow levels. The reason for the change is probably to make search results more relevant. Improving search results is an overarching goal for the Google team, and algorithm and formula changes are ongoing as a result.

While PageRank may not be the most important or even a major portion of the Google algorithm, it still carries some weight. The Google algorithm, especially since the infamous “Florida update”, has placed more emphasis on links, link anchor text, and relevance. The changes to the PageRank formula reflect those alterations as well.

Topic-Sensitive PageRank is a theoretical attempt to make the system of PageRank potentially more accurate. Instead of a single PR ranking, the TSPR calculation would create several different PageRanks for each particular topic. The topics used for the tabulations would be representative of the theme of each specific web page.

The idea would be to use a number pre-calculated and topic-biased vectors to create a number of PageRanks for each web document. In that sense, the PR would be theme sensitive.

Instead of the PageRank being based on all incoming links, the Topic-Sensitive PageRank would be heavily weighted toward links that were related to the page’s main subject area. Links from sites not directly on topic with the specific web page would be assigned much less weight in the calculation.

In the Topic-Sensitive PageRank system, heavily linked pages bearing no informational relationship with the search term will be given less weight for that topic. On the other hand, pages receiving only a few incoming links, but from very related sites, will be given much more consideration for that term. The result will be a higher TSPR for that site, for that specific search query, despite a much lower PR under the current system.

Similar to the previously used Google PageRank system, the Topic-Sensitive PageRank might also be pre-computed, to save time in the search query processing. Since there are multiple themes to calculate, each page would be scored against multiple topics. Instead of one PR number, there would be many numbers based on the total number of themes used in the computation. That appears to many Google observers to be what is happening with PageRank calculations at the present time.

Keeping these additions to the original Google PageRank formula in mind, we have a much more complex system of calculations being utilized at the present time.

A very basic and highly simplified example might help to explain the newly implemented process. Keep in mind that the numbers used are purely for illustration and are in no way indicative of the actual formula. They are only to show the importance of topic to the new PageRank calculation.

A sending page with no topic relationship at all to the receiving page, divided among many outgoing links would transfer PageRank of 1 point. The PageRank passed along would be the minimum amount.

A donor page with no topic relationship, but few outgoing links, might transfer 2 points.

Having a topic relationship with the receiving page, but with the outgoing page dividing its PageRank between many links, might pass along 3 points of PageRank.

A page with close topic relationship to the catchment page, and few outgoing links, might send along 4 points of PageRank.

As seen in the theoretical example, topic relationship is vital to the newer PageRank formula. The number of outgoing links from the page remains, as always, an important factor in the calculation. Nothing has changed in that respect. The more ways the donor PageRank has to be divided, the less power there is to go around.

Conclusion

There is little doubt among search engine professionals that the method of calculating Google PageRank has changed over time. The mystery remains, however, in how the formula is currently being applied.

Clearly, the original PageRank formula has been replaced. The newer mathematical basis is quite likely Topic-Sensitive PageRank based. That means, in its most simple form, that pages with similar content will help another web page much more than pages with no topic relationship at all.

The refinement of the PageRank formula is an ongoing process at Google. In their attempt to make PageRank more relevant and to remain a viable part of their overall search algorithm, the Google engineers continue to fine tune their calculations.

Expect more changes to the PageRank formula over time. Those alterations will likely be made with a goal of being more topic sensitive to the receiving page.

Keeping those theme and topic relationships in mind when adding incoming links will help the careful website owner achieve the most benefit from the new Google PageRank formula.

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