Facebook Inc (NASDAQ:FB) has been accused of fraudulent activity by many investors since its initial public offering in May. One analyst, Janet Tavakoli from Tavakoli Structured Finance, looks at fraudulent user numbers on the firm’s social networking site in a new report. Using some simple math, Tavakoli comes to some startling conclusions.

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The full report, in pdf, can be found here.

In the prospectus for the Facebook Inc (NASDAQ:FB) IPO, Facebook reported that an estimated 5-6% of its Monthly Active Users were fakes, as of December 2011. Fake users are defined as accounts presenting false information. In a filing for the period ending June 30, 2012, Facebook reported its estimate of fake MAUs at 8.7%.

According to the report, there are only two possible explanations for the vast increase. The first is that the growth in fraudulent use of the social network spiraled upward at a frenetic pace in the weeks following the IPO. The second is that those numbers were under reported in the IPO prospectus.

There is at least one other possible explanation. Facebook Inc (NASDAQ:FB) might have changed its practice in estimating falsified usage in the days immediately following the IPO. The company has not revealed any such change publicly.

Depending on how Facebook Inc (NASDAQ:FB) calculates the number of fake MAUs, there can be a large discrepancy in the perceived amount of fraud on the social network. For example, with a fraud rate of 8.7% and a user base of 955 million, as reported for the period ending June 30, Facebook could have a total number of fake MAUs of 83 million, or, if the firm removes the fakes before reporting user figures, 91 million.

As Tavakoli points out, depending on the way Facebook reports these numbers, it can have a significant impact on the perceived fraudulent activity on the website.If Facebook has not changed the way in which it calculates its fraudulent users in any way, the growth in fake use is staggering.

According to the analysis, relative to the December 2011 figure of 5-6% fake MAUs, the June 30 2012 numbers show a growth rate of 64-97% in fake account usage. If Facebook subtracts the numbers of fake users before reporting its user base, the growth rate is 69-104%.

According to Janet Tavakoli, “No matter how you look at it, at  the time of its IPO, Facebook either under reported the fraud problem, or the fraud growth soared. When was Facebook first invaded by this “new” herd of the walking dead? If Facebook  didn’t under report, then why is fraud soaring?”

These are appropriate questions indeed, and ones Facebook Inc (NASDAQ:FB) should respond to if its shareholders begin to ask them. The questions come at a time when stock is recovering at a steady rate. The firm’s shares, having started the  month trading for around $21, are now trading above $27.

The report from Janet Tavakoli, available on her website, contains many more questions than these about Facebook Inc (NASDAQ:FB)’s business performance and practice. It forms a credible opposition to a recent slew of reports supporting the firm’s stock recovery.

Facebook Inc (NASDAQ:FB) may not have committed grievous fraud, but it should answer for the way in which these numbers stack up. It will be up to shareholders to ask those questions of the world’s largest social network.

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