The Importance Of Internal Link Structure In SEO
The various link popularity algorithms used by Google would take a professor to explain as they are steeped in arcane forms of mathematics and statistical probabilities. What you should know about link popularity is that each and every page is treated as a completely separate object. The internal links that you have within your site carry significant weight as the algorithms generally don't make any form of clear separate distinction between an interior and an exterior link.
Admittedly, it is very difficult for an algorithm to make a conclusive determination of an internal link from an external one as many sites are spread over a number of separate and multiple domains and sometimes even on separate hosts, but it does at first seem like a glaring omission from the learned mathematicians at Google who have been able to readily conquer other rather obscure and tenuous factors that could lead to a skewing of their results. The algorithms have worked out a very reliable way to tell an artificial linking scheme from a real one, so it would seem to follow that they could also determine an interior link from an exterior link.
What that tells the web site owner and publisher is that significant attention should be paid to internal links as they can have an inordinate effect on the final Page Ranking of the entire site. The quality of the link as determined by the algorithm has a direct effect on the Page Ranking far above the sheer number of links, which could also be counterproductive in some cases. Quality impacts on almost all the decisions that lead to a determination of Page Ranking.
The algorithms can determine whether the content in your site is "important" and the exact structure that such content has in relationship with the pertinent keywords. If the sites that are linking to you feature most of their keywords in unrelated fields of endeavor, then the linkage is discounted as it is not directly relevant. The Google Page Rank wants to see relevant information linking to other relevant information, so that the visitor following these links can drill further and further down into the particular topic of interest, not be redirected horizontally to subject matter that is not directly related and may be of minor or no interest to the reader.
The algorithms look at pretty well everything on the page in order to make their ranking determination. The headers, the page titling, the text that surrounds the link as well as the text which is contained in the link itself are all scrutinized for relevance. It is important to have a keyword-dense heading and title on your page, but please remember that humans have to read it too, and what will be a nicely keyword-packed title to a bot may not be so readable nor understandable to a person. Therefore, if you have a heading of "Caribbean Cruises: Cruise to the Caribbean on a Cruise ship to all Caribbean Cruise ports in the Caribbean Sea" you're shooting yourself in the foot. Don't laugh. I've seen worse!
All of this information should be incorporated completely throughout your site to maximize the effectiveness of the Google algorithms' processing of the internal links of your site and the corresponding Page Ranking that it will give your site.