Just think about any relationship for a moment. How long you've known a person is incredibly important. It's not the be-all-end-all, but it is fundamental to trust. If you've known someone for years and years and other people that you know who you already trust can vouch for that person, then you're far more likely to trust them, right? But if you've just met someone, and haven't really vetted them so to speak, how can you possibly trust them?
Today, with nearly half the world's population wired to the internet, the ever-increasing connectivity has created global shifts in strategic thinking and positioning, disrupting industry after industry, sector after sector. Seemingly, with each passing day, some new technological tool emerges that revolutionizes our lives, further deepening and embedding our dependence on the world wide web.

I am not worried by this; I do agree with Danny Sullivan (Great comment Danny, best comment I have read in a long time). I will not be changing much on my site re: linking but it is interesting too see that Google took over a year to tell us regarding the change, but was really happy to tell us about rel=”nofollow” in the first place and advised us all to use it.

If Google finds two identical pieces of content, whether on your own site, or on another you’re not even aware of, it will only index one of those pages. You should be aware of scraper sites, stealing your content automatically and republishing as your own. Here’s Graham Charlton’s thorough investigation on what to if your content ends up working better for somebody else.
The SEO industry changes at an extreme pace, every year marketers evolve their strategies and shift their focus. However, backlinks remain just as crucial of a strategy as when they were first created. Currently, backlinks are a very common phase in the world of SEO, and if you are involved in the industry, you know backlinks are vital to a website’s performance.
Now, back to that webmaster: When reaching out, be friendly and introduce yourself. Tell this individual that he or she is linking to some resources that are no longer available. Always provide the exact location of the broken links, so they can be easily found. Give some alternatives to replace those links, including your own website. Try to be helpful, not greedy to get a backlink. Often, this method will work, but there will be cases when the webmaster will refuse to link back to you.
The green ratings bars are a measure of the importance Google’s assessment of the importance of a web page, as determined by Google’s patented PageRank technology and other factors. These PageRank bars tell you at a glance whether other people on the web consider Google considers a page to be a high-quality site worth checking out. Google itself does not evaluate or endorse websites. Rather, we measure what others on the web feel is important enough to deserve a link. And because Google does not accept payment for placement within our results, the information you see when you conduct a search is based on totally objective criteria.
Secondly, nofollow is also essential on links to off-topic pages, whether they’re internal or external to your site. You want to prevent search engines from misunderstanding what your pages are about. Linking relevant pages together reinforces your topic relevance. So to keep your topic silos clear, strategic use of the nofollow attribute can be applied when linking off-topic pages together.
Something a lot of people seem to have overlooked was hinted at in Greg Boser’s comment above. Greg identified that there is a major (and unfair) disparity with how authority sites such as Wikipedia disrupt the linkscape by run-of-site nofollows. Once Wikipedia implemented the no-follows, previously high-value links from Wikipedia were rendered worthless making the site less of a target for spammers. Increasingly large sites are following suit in order to cleanse their own pages of spam.

When Googlebot crawls a page, it should see the page the same way an average user does15. For optimal rendering and indexing, always allow Googlebot access to the JavaScript, CSS, and image files used by your website. If your site's robots.txt file disallows crawling of these assets, it directly harms how well our algorithms render and index your content. This can result in suboptimal rankings.

When referring to the homepage, a trailing slash after the hostname is optional since it leads to the same content ("https://example.com/" is the same as "https://example.com"). For the path and filename, a trailing slash would be seen as a different URL (signaling either a file or a directory), for example, "https://example.com/fish" is not the same as "https://example.com/fish/".

On another note, I would like to express my contempt for Google and its so called terms of service regarding the legitimate acquisition of links. why should it care if links are paid for or not? Thanks to the invention of pagerank, it is Google itself that has cancelled out reciprocal linking and has stopped people giving out links due to fear of them losing pagerank, and blogs and forums are worthless thanks to the nofollow trick. so it is now impossible to get decent links organically, without having to pay for them, and those who do give out free links are considered fools. Google has brought this dilemma on itself, and yet it seems like punishing us for trying to get links other than freely! Face facts, no one is going to link to someone without getting a link in return! google has invented pagerank which is like a currency, and so people expect to be paid for links, as giving out links devalues their pagerank and so compensation is now required. It is forcing people to use underhand methods to get links, mostly the ‘paid’ variety.
Most schools / universities have just an [email protected]… or [email protected]…. email address, which goes to the reception. I don’t really know who to address this email to, as I believe a lot of the time the admin person receiving it ignore and delete it without passing it on to someone relevant, e.g. the school’s or universities’ communications manager. Hope you can help me on this one! Thanks so much in advance!

Early versions of search algorithms relied on webmaster-provided information such as the keyword meta tag or index files in engines like ALIWEB. Meta tags provide a guide to each page's content. Using metadata to index pages was found to be less than reliable, however, because the webmaster's choice of keywords in the meta tag could potentially be an inaccurate representation of the site's actual content. Inaccurate, incomplete, and inconsistent data in meta tags could and did cause pages to rank for irrelevant searches.[10][dubious – discuss] Web content providers also manipulated some attributes within the HTML source of a page in an attempt to rank well in search engines.[11] By 1997, search engine designers recognized that webmasters were making efforts to rank well in their search engine, and that some webmasters were even manipulating their rankings in search results by stuffing pages with excessive or irrelevant keywords. Early search engines, such as Altavista and Infoseek, adjusted their algorithms to prevent webmasters from manipulating rankings.[12]

Personally, I wanted a bit more of the math, so I went back and read the full-length version of “The Anatomy of a Large-Scale Hypertextual Web Search Engine” (a natural first step). This was the paper written by Larry Page and Sergey Brin in 1997. Aka the paper in which they presented Google, published in the Stanford Computer Science Department. (Yes, it is long and I will be working a bit late tonight. All in good fun!)
Page rank is an assessment of the authority and value of a website in Google’s algorithm. You can find plug-in tools for your browser or online tools (see the references section for links to some of these) to check the page rank of any given site. You can also check your own website’s page rank. The higher the page rank, the more likely it is that your SEO efforts are succeeding.

A generalization of PageRank for the case of ranking two interacting groups of objects was described in [32] In applications it may be necessary to model systems having objects of two kinds where a weighted relation is defined on object pairs. This leads to considering bipartite graphs. For such graphs two related positive or nonnegative irreducible matrices corresponding to vertex partition sets can be defined. One can compute rankings of objects in both groups as eigenvectors corresponding to the maximal positive eigenvalues of these matrices. Normed eigenvectors exist and are unique by the Perron or Perron-Frobenius theorem. Example: consumers and products. The relation weight is the product consumption rate.
Keyword analysis. From nomination, further identify a targeted list of key­words and phrases. Review competitive lists and other pertinent industry sources. Use your preliminary list to determine an indicative number of recent search engine queries and how many websites are competing for each key­word. Prioritize keywords and phrases, plurals, singulars and misspellings. (If search users commonly misspell a keyword, you should identify and use it). Please note that Google will try to correct the term when searching, so use this with care.
You’ve launched an amazing product or service. Now what? Now, you need to get the word out. When done well, good PR can be much more effective and less expensive than advertising. Regardless of whether you want to hire a fancy agency or awesome consultant, make sure that you know what you’re doing and what types of ROI to expect. Relationships are the heart and soul of PR. This chapter will teach you how to ignore the noise and focus on substantive, measurable results.
Business address listings on Google, Yelp, LinkedIn, Facebook, Yellow Pages, and elsewhere count as backlinks. Perhaps more importantly, they also go a long ways towards helping customers find your business! There are many, many such sites. A good way to approach this once you've gotten the biggies out of the way - Google should be your first priority - is to make a point of setting up a couple new citation profiles every week or so. Search around for updated lists of reputable business listing sites, and use it as a checklist.
But I also don’t wanna lose PageRank on every comment with a link… If I can give PageRank and lose none, I wanna let the comment there, even without nofollow. But if I lose PageRank on every link, even inside original post, EVEN MORE if nofollow also takes PageRank out of me, I may just start using JavaScript or simple text without anchor for links… I definetely don’t like this idea, but I dislike even more losing PageRank on each outlink on my site. I’d just link top quality sites that I actively wanna vote for Search Engines.