How does Google verify the trustworthiness of a website?
How does one create trust with Google?
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Google looks at the quality of the domains linking to you (.edu links are highly prized) and if they are trustworthy. Peer reviewed directories help as well.
Other factors include having the domain for a couple years and preregistered for a couple years in the future as well.
Businesses can look to increase trust by having BBB links, Chamber of Commerce, and Places verified.
Inbound links from social sites (tumblr, twitter, facebook, google+) help as well.
Google's algorithms are naturally closely guarded, and they claim over 1,000 factors go into ranking sites. That said, the following are believed to be important quality indicators:
1) Links - both number and type. Links from other high-quality domains are what you want, especially if they're from relevant sites; that is, if I have a pet site, links from other animal sites will be more relevant than a link from a t-shirt site.
2) Age - newer sites often have difficulty ranking over older sites (although brand new sites will get a bump for a short time)
3) Size - Longer pages are preferred over shorter ones (although this doesn't mean that very short pages can't rank well). Google tries to figure out if your page is providing the user with what he's searching for.
4) Keywords - not in the meta tag, Google doesn't care about that, but in the page itself. If I'm writing about dogs, Google might expect to see the words pet, walk, leash, etc...in other words, certain terms will tend to come up naturally when you're actually writing for the user rather than the search engine. (So write for the user!) Avoid keyword stuffing, or repetively using the same keywords over and over to try to rank higher; this is a sign of spam.
5) Load time and bounce rates - if the user immediately hits the back button, or if your site takes eons to load, your page will be downgraded.
6) Outgoing links - you're judged by the company you keep. Don't link to spammy sites!
Another factor which I have noticed after Google Panda update is that Google is discounting sites with a general theme. For e.g. Buzzle, Squidoo which covers everything under the sun and sea have lost a great amount of traffic in last few months. On the other hand, sites with a specific niche are converting better in SERPs.