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Basically link popularity involves quantity and quality of links from sites external to yours
It is better to have sites with high PR (Page Rank), because google considers high ranked sites to be "authorative", which is mostly due to the fact that many sites have linked to it, or other authorative sites have linked to it.
For instance, if one day you amazingly managed to get a link on the home page of google, your "link popularity" would skyrocket, because the web as a mass (the way google perceives link popularity) would mean that your site is an authorative area of the web
Hope that didnt sound too confusing. Im late and tired :) Others will have plenty to say about it (all u link pop hunters ;) ......and the site search up to the top left of the screen will uncover plenty more info on the subject
The more links there are to your site, the higher your popularity becomes. You transfer popularity value to the websites you link to - the more websites you link to, the lower the value of the link.
Factor into that the fact that search engines are working out subject-specific popularity - i.e., presumably having a link from a website that is related semantically to yours will help more than having a link from a random website.
Google also factors in the words included in the link to your site. So, if you are in the Internet marketing business, then having links to your site that have the words Internet marketing in the link will help even more. It goes on and on and gets more and more complicated.
The thing to take away is the fact that you need links back to your website from other websites. Even if popularity weren't considered, you would be giving your site more and more chances to be found and re-spidered.
Linda, it can be a challenge to find good links. In your case, it might be good to start looking for not competing, but complementary sites in your locality to exchange links with. Find businesses that have related services, with a connection to consumers who would likely use their services and yours, both.
A good place to start is ODP [dmoz.org] or Google's directory, looking for appropriate companies and possibly directories and portals that are local to your area.
[marketleap.com...] is a good resource to compare your link popularity as well as showing how many pages of your site are indexed.
Your link popularity is extremely dependent on pages being indexed at a search engine, your pages as well as pages that are linked to you. A good rule of thumb - "a search engine is only as good as what it can (see) connect to". If a page of your site has 1,000 links to it but not indexed then according to that search engine those links do not exist.
In this case you would have a less "authorative position in the web" as Bortherhood of LAN indicated.
As you develop your link strategy indexing becomes increasely important.
Rod