Gaining high link popularity is perhaps the single most important factor when trying to reach the top page on the major search engines. It appears all the large SEs are using link popularity as a way of calculating the importance of a page, thus giving it a higher rank.
Some people in the SEO business argue that link popularity is widely overrated, and are instead claiming the relevance of the link to be of much more importance when calculating the final SE position. According to this theory, a few links from highly relevant pages would mean much more than many links from pages with lower relevance to your website.
Other SEO theorists argue link popularity to be the single most important factor, and are often using nothing but the anchor text (the word or phrase actually linked) to target their keywords and phrases. According to this theory, one could reach a high SE position by a massive amount of links with keyword rich anchor texts.
Using any of these techniques will surely raise both your link popularity, and your SE position, but I see little reason not to go both ways. If getting many links would improve your ranks, and a few relevant would as well getting them all would surely improve your ranks even further.
Link popularity, and links of lower relevance, can serve as a major source of search engine traffic for some often larger sites. A large site is bound to have quite a few topics, and even more possible phrases people could use to find them. With many links, your will have some words or phrases targeted by accident, bringing you more of those precious visitors. Generally, the more subjects you cover, the better you will serve from high link popularity, even though all sites benefit from more backlinks. Be sure to use keyword rich anchor text, as thats your only way of targeting specific words.
Using only a few relevant links will naturally only boost the SE positions for words and phrases used on those pages, preferably near your link. If you instead are building mini- or micro sites, targeting only one, or a few specific keywords, relevance would be a much faster way to improve your ranks for those searches. A few articles containing your keywords, along with a few good links, might be enough to get you on top for non competitive search terms. For more lucrative areas, you will need to work harder.
Getting relevant links tend to much more time consuming, as this often is done manually. Searching the web for potential link partners tends to take some time, but done correctly, its a powerful way of marketing your site. Finding links of low, or no relevance can be done in a much faster manner, but the amount of links needed is much higher. Depending on niche, size of site and other factors, choosing one way or the other might work; but using both methods will get you higher positions in every major search engine.
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