Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.
When we talk about ad links, we're not talking about search ads on Google or Bing, or social media ads on Facebook or LinkedIn. We're talking about sites that charge a fee for post a backlink to your site, and which may or may not make it clear that the link is a paid advertisement. Technically, this is a grey or black hat area, as it more or less amounts to link farming when it's abused. Google describes such arrangements as "link schemes," and takes a pretty firm stance against them.
In my experience this means (the key words are “not the most effective way”) a page not scored by Google (“e.g. my private link” – password protected, disallowed via robots.txt and/or noindex meta robots) whether using or not using rel=”nofollow” attribute in ‘links to’ is not factored into anything… because it can’t factor in something it isn’t allowed.
These are ‘tit-for-tat’ links. For instance, you make a deal with your friend who has a business website to have him place a link to your website, and in exchange your website links back to his. In the dark ages of SEO, this used to be somewhat effective. But these days, Google considers such 'link exchanges' to be link schemes, and you may get hit with a penalty if you're excessive and obvious about it. This isn't to say that swapping links is always bad, but if your only motive is SEO, then odds are that you shouldn't do it.
A Web crawler may use PageRank as one of a number of importance metrics it uses to determine which URL to visit during a crawl of the web. One of the early working papers that were used in the creation of Google is Efficient crawling through URL ordering, which discusses the use of a number of different importance metrics to determine how deeply, and how much of a site Google will crawl. PageRank is presented as one of a number of these importance metrics, though there are others listed such as the number of inbound and outbound links for a URL, and the distance from the root directory on a site to the URL.
I’m done. Done worrying, done “manipulating”, done giving a damn. I spent 10 years learning semantics and reading about how to code and write content properly and it’s never helped. I’ve never seen much improvement, and I’m doing everything you’ve mentioned. Reading your blog like the bible. The most frustrating part is my friends who don’t give a damn about Google and purposely try to bend the rules to gain web-cred do amazing, have started extremely successful companies and the guy following the rules still has a day job.
For example this page. My program found almost 400 nofollow links on this page. (Each comment has 3). And then you have almost 60 navigation links. My real question is how much percentage of the PageRank on this page gets distributed to the 9 real links in the article? If it is a division of 469 which some SEO experts now are claiming it is really disturbing. You won’t earn much from the links if you follow what I am saying.
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