Google does update periodically, but there is no preset time or period in which this is done. Typically, Google will roll over updates on backlinks and page rank on its data centres when a complete index update and review has been completed on indexed documents and document integrity on that centre.
Because Google has lots of data centres, page rank updates happen quite far apart, sometimes in excess of 3 - 6 months.
The important thing is to focus on building your websites link profile, do not try and quantify early on, one month of hard link building won't always give you what you'd expect, especially since Google will not release all link information.
Keep building links, create some good link bait, some website tools and resources, and share something with the public, this is more likely to attract more natural backlinks.
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