It’s been exactly one month since Google+ made its debut. The social network was designed to be more than just Google’s response to Facebook; it’s “an extension of Google itself,” as Google SVP Vic Gundotra told us before launch. After the failure of Google Wave and Google Buzz, Google+ is the search giant’s last best chance to grab a piece of the social-networking pie.

So one month in, how’s it doing?

Pretty well, by most accounts. Google+ has become the fastest-growing social network in history. Thanks to a fair number of positive reviews, it has acquired more than 20 million users — a phenomenal accomplishment by any standard.

At the same time, there are signs that Google+ is losing steam, and that it could have an early adopter problem.

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