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For example, at the end of some articles in some online magazines they'll have a small "related links" section with links to other articles within that site covering similar topics to that which was covered in the article on that page. Do these links increase the link popularity to the page they target? Personally, I'm think yes from my unscientific tests on Google. Anyone here have a more solid answer to this?
It is my feeling that you are talking about two different subjects. And while they both have an effect on a site's ranking and SEO, they are still two different topics.
Link Popularity is the number and quality of external links that point to your website and webpages.
What you are talking about is the internal linking of your website. There is a certain method of internal linking that should be applied to achieve the best results.
When you are talking Google, an internal link from a page with higher pagerank does add to the pagerank of the targeted page. But this is a special Google concept.
In engines that go for theming itīs a good idea anyhow to link related content together.
But the term linkpopularity, as agerhart explained, usually is applied to external links only.
Some engines are thought to give more weight to external links, and some people believe that Google might tweak their scoring in that direction but there's no evidence of that having happened yet.
Internal linkage is one of the ignored aspects of SEO.
Calum
Spiders crawl on links, the better the spider is able to crawl your site the better the result.
I try to make every page accessable in max 2 cliks and I try to make sure that a user easily can find related content on my pages.
To say it short, a spider will feel more at home in a web of links. Hope this helps