Google’s social network, Google+, might be one of the fastest-growing networks ever, having already reached 10 million users according to one estimate.

Paul Allen, of Ancestry.com – not to be confused with Microsoft co-founder Paul Allen – has developed an interesting methodology to calculate the number of Google+ members.

He sampled a number of surnames from the U.S. Census Bureau data and compared it to surnames of Google+ users. By comparing surname popularity in the U.S. with the number of users on Google+ with each surname, he can guesstimate the percentage of the U.S. population that signed up for Google+. Finally, he calculated a ratio of U.S. to non-U.S. users to generate an estimate for the number of Google+ users worldwide.

The result? According to Allen’s estimates, Google+ has approximately 9.5 million users worldwide, with 2.2 million joining in the past 32 to 34 hours.

This is amazing growth even for a giant such as Google: We cannot remember any social network reaching so many members so quickly after its release.

Coming from a third party, the data is obviously unofficial (we asked Google for comment on these numbers, but haven’t yet heard from them) and should be taken with a grain of salt. If they’re true, though, they indicate that – after so many stumbles – Google might finally be conquering the social networking arena.