I can say, it belong to many factors, but still, for a very quick look you can think the alexa rank base on the number of traffic of a website in 3 months, the google rank base on the website trust and quality and pagerank index only 2 or 3 times/year but alexa rank index daily.
Let 's get an example about
http://magentoexpertforum.com
At a moment:
Alexa rank: 104k
Google pagerank: N/A
The reason why it have no google pagerank because the domain old still too young even though the traffic is good. The last pagerank index of Google pagerank is Feb 2013 and it still doesn't index again until now. But with some SEO tools for pagerank look ahread, you can easy realize page rank for next index of this is ~4
Hope it help you in the complicated numbers.
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