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What is Pagerank flow anyway?

What's your model?

         

SlyOldDog

9:45 am on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



I like to analyse mathematical models with a real life analogy.

For example, I always imagine electricity as flowing water from high ground (high voltage) to low ground (low voltage). Capacitors are like reservoirs which fill with water, but overflow if they get too full (discharge).

This model got me through school fine and always helped me when I was confused.

However, this model doesn't work for PageRank becuase PageRank gets "stuck" on a page, and doesn't flow away. Once a page has pageRank it can't lose it, all though it can pass a carbon copy of that pagerank (or a share of it)to another pager.

I can't think of a real life analogy for PageRank. Hs anyone got one?

killroy

10:12 am on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



think of a page as a bucket. the PR is like a high water mark. Watrer fills it (links in) the high water mark goes up (PR) water flows out into other buckets (links out) and passes votes to other buckets (increasing their high water mark). The high water mark never goes down on it's own.

Of course now you havce to imagien a strange universe where all teh inflowing happens FIRST (so the high water mark gets established) before all the outflowing is done :) Hmm back to the drawing board of mind models.

SN

dirkz

10:46 am on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



Why not see PR as water flowing through the whole WWW, the more PR a site "has" the more of it is hold back on the page (dammed up) before flowing on.

PR slows down the flow of the water.

A link eventually gives PR a way to flow further.

michael heraghty

1:17 pm on Sep 29, 2003 (gmt 0)

10+ Year Member



As the punchline to the old Irish joke goes, "Well, I wouldn't start from here."

i.e. I think that you're implicity looking for a physics analogy, but I think a metaphorical model for PR is more likely to come from social science, e.g. statistics, population theory, or perhaps even macrobiology e.g. swarm theory...

jcoronella

1:23 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



[iiinnnhale... hold. hold. eexhale...]

Well, keeping with the water analogy. I think you could see each site as a bucket, and a whole in the bottom of the bucket as an external link. PR is the amount of water flowing into any bucket. A bucket with a lot of other buckets dripping into it, can support more holes in the bottome of it to support other buckets below it and maintain enough water to have PR without having it flow out the bottom.

The problem with this analogy, is that it's easy to envision PR as the amount of water, but really PR is the amount of water flowing into a bucket, and has no relation to how much water is actually in the bucket.

Of course, water would aslo have to drip up.

rfgdxm1

3:05 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



>i.e. I think that you're implicity looking for a physics analogy, but I think a metaphorical model for PR is more likely to come from social science, e.g. statistics, population theory, or perhaps even macrobiology e.g. swarm theory...

Probably the best answer. Best I can think of is the following. Janey and I are at a social gathering. Janey says that she has a degree from Harvard University. I say that I have a degree from Saginaw Valley State University in Michigan. Typically people will consider where Janey mentions having gone to school far more impressive. Even without knowing our grade point averages, etc.

And, I just looked it up. Home page of harvard.edu is PR 9. www.svsu.edu is PR 6.

TheWhippinpost

3:33 pm on Sep 29, 2003 (gmt 0)

10+ Year Member



<shot-in-the-dark>
Think of all the Greats through time; Edison, The Wright Brothers, Einstein, Newton, Frank Zappa :) etc...

These "entities" became deferred to, borrowed from and expanded upon by "lesser entities", ie... from their Great Works came a myriad of spin-off "entities", each commanding respect and authority in their own right but at the same time casting a nodding vote back to the "Prime-Movers".

Hey, it looks good in me head, honest!

plasma

3:35 pm on Sep 29, 2003 (gmt 0)

10+ Year Member



Apart from PR coming through inbound links, each site or link must have a (possibly infinitesimal) small PR.
The other possibility is that somewhere is a PR-Singularity (maybe some trusted sites, authority hubs, directories) where all the PR comes from initially.
Everything else would lead to a chicken-egg problem.

SlyOldDog

4:22 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



The social analogy has been expanded on quite a lot on WebmasterWorld, and even the Google founders talk about PR as "votes". Something like:

If someone famous gives me a reference it makes me famous too. But if he gives loads of people references that will make me less famous because people will get bored of listening to him.

The problem is that this model doesn't handle feedback in a visible way.

I liked jcoronella's buckets and quantity of water flowing model, but it still has holes (pardon the pun).

Imagine a direct current electrical circuit board dotted with resistors (sites). Each resistor (site) can feed off to other resistors (sites) with a straight wire connection. The pagerank is equivalent to the current flowing through the resistor. High current = high pagerank. Of course it's possible to link back to a site further back in the chain by just making an electrical connection to it's input from your site's output.

Hmmm. Time for a coffee....

Edit: Just realised the feedback wouldn't work for resistors. So replace those with transistors...I think it's easier to understand the mathematical model ;)

[edited by: SlyOldDog at 6:56 pm (utc) on Sep. 29, 2003]

rfgdxm1

4:30 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



>Apart from PR coming through inbound links, each site or link must have a (possibly infinitesimal) small PR.
The other possibility is that somewhere is a PR-Singularity (maybe some trusted sites, authority hubs, directories) where all the PR comes from initially.
Everything else would lead to a chicken-egg problem.

The answer for you plasma is each page starts out with a small value of PR. This is mentioned in the original academic papers. Since all pages start out with the same seed PR, none have an advantage over the others at the start. It is when sites start linking to each other that PR differences come in.

plasma

4:34 pm on Sep 29, 2003 (gmt 0)

10+ Year Member



The answer for you plasma is each page starts out with a small value of PR. This is mentioned in the original academic papers. Since all pages start out with the same seed PR, none have an advantage over the others at the start. It is when sites start linking to each other that PR differences come in.

Then theoretically someone could bootstrap a high pr himself without anybody else linking to him just by having thousands of pages that all link to 1 page.
Scaring.

rfgdxm1

4:49 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



I believe plasma that Google deals with that possibility by only allowing seed PR to flow with links to other sites.

willybfriendly

4:51 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



The Internet is a river of information, constantly flowing. The currents are always changing, and as they change, they in turn change the course of the river via erosion and sedimentation.

PR is like water cascading down a mountain from pool to pool. Larger pools contain a larger flow of the water. Their source is either a few very large "streamlets", a lot of small "streamlets" wending around rocks and logs, or a commbination of the two.

PR changes as the channels and currents of the Internet change. It can be a natural process of new channels being opened via erosion and sedimentation (i.e. a rock is dislodged or a bank caves in, resulting in more flow to an existing pool) or it can be accomplished by direct intervention (i.e someone gets in and manually creates a new channel in the stream.)

Stream flow shanges with the seasons, and sometimes with the hour of the day. When the water is high, new pools may form along the edges. Given enough flow, time and erosion, the bed of the stream may shift, leaving old pools to gradually evaporate.

Fluid dynamics might be the model you are seeking.

The fish (consumers) like the deep, quiet pools. As anglers, we must either fish the quiet stretches of the river, or entice the fish into risking a move to a smaller, more turbulent stretch.

WBF

dirkz

4:52 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



Then theoretically someone could bootstrap a high pr himself

Exactly. But don't forget that your chances of getting into Google's index is going to nil if no one's linking to you.

But this is exactly what some sites do (in some variations): Get one free link from an unrelevant site (ffa, GB etc.) and then inflame a whole PR network with 30,000 generated pages.

plasma

4:52 pm on Sep 29, 2003 (gmt 0)

10+ Year Member



I hope so, on the other side, Google indexes pages not sites.

dirkz

4:58 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



Do you know SimCity? Those streets viewed from above crowded with cars? :)

I could imagine PR flow similar like the flow of traffic. On high PR sites there are a lot of PR cars, on low PR sites there is only occasionally one car. No hen-egg problem because PR is like visitors everywhere and does not start anywhere, nor stop.

vitaplease

7:03 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



Eventually every webpage is a star in the galaxy.

Every star selectively gets light radiated towards it from certain other star(s).

The more light radiated the more shiny, bright and important the star becomes.

That could be small amounts of light from many unimportant stars or one beam from an important star.

In turn every star selectively mirrors out 85% of all incoming light to other star(s).

Every star can choose to evenly radiate out its slightly dampened light to (n)one or more stars.

very funny Googleguy, now beam down my real PR

plasma

7:08 pm on Sep 29, 2003 (gmt 0)

10+ Year Member



The more light radiated the more shiny, bright and important the star becomes.

Then WW sends out Gamma Ray Bursts ;)

farnwomt

7:24 pm on Sep 29, 2003 (gmt 0)

10+ Year Member



I am not convinced that water really works for this, it would work far better to talk about people being famous.

People are famous because lots of little people talk about them, or maybe because a few famous people talk about them. Ultimately everything is pinned on the little person though, without those little people there would be no famous people.

You don't become less famous by talking about somebody else (just like you don't lose pagerank by linking to somebody), but if you are selective in who you talk about and they go on to talk about you as well it can help your own fame.

In this analogy a person is a webpage (not a website).

TheWhippinpost

7:25 pm on Sep 29, 2003 (gmt 0)

10+ Year Member



Imagine being in a nightclub; There are a handful of very attractive, nubile and highly PRomiscous girls...

:ŹD

steveb

10:57 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



It is all about water. Bad PR use is bucket-oriented. Bucket PR is thinking in terms of overflow and excess.

PR is like the oceans and rivers of the world. Good use of PR is to make hydroelectric power plants as the river flows through your community. Bad PR use is hoarding it, letting it lay stagnant in a pool, unused. Good PR is using the water again and again, letting it flow, sharing it, getting it back. Good PR use is diverting it into this field or that one, depending on whether you are planting summer corn or winter wheat, changing it back when the season's change.

kaled

11:48 pm on Sep 29, 2003 (gmt 0)

WebmasterWorld Senior Member 10+ Year Member



Imagine every page to be a tower of bricks. If a tower is 500 bricks tall, it is allocated, say, 500 bricks that it can donate to other towers (but not itself). By linking to other towers, they become taller. In turn, if they link back to your tower, it becomes taller. PR is thus calculated iteratively. However, in this model, on each iteration, towers would continue to get taller and taller so you have to tweak the maths to prevent this.

Kaled.

PS
It is possible that pages (towers) are allocated some bricks for use within the website and other bricks for use outside the website.