There is so little information about Bitcoin's "fundamentals" that can be gleamed. Even the basics, such as "how many bitcoins were spent in the past 24 hours" are nearly impossible to even estimate. There is a raw number showing the number that transferred but that includes change transactions so even that most basic of all metrics needs some subjective analysis before a usable number is available.
Charting the data might show trends that are useful and somewhat accurate ... such as, the number of transactions per day
There are fuzzy metrics, such as the number of merchants on the Bitcoin trade page that will show if Bitcoin is gaining traction. There are many who rely on even less relevant metrics, such as the Google trends search volume numbers.
If the market is always right, then the metric that shows bitcoin's health is the current exchange rate. Right now the market believes that Bitcoin digital currency is worth currently a little over $50 million, though the reason each participant holds bitcoin and doesn't sell at the current price will vary from one individual to the next. The take away is that bitcoin is unlike nearly any other asset class ever seen. Determining its value will be an exercise that is even more difficult than most any other.
I'm also thinking a statistical analysis of the address balances could be useful here. E.g. median or mode (binned data) plotted against time could give you a sense of how the number of users is changing, skewness could give you a sense of diffuseness of the bitcoin distribution, etc.
Do you know if anyone has done this?
Of course if any of these become widely used for valuation then people would start gaming them. It might be possible to get really creative with statistics and graph theory and detect this, though. Who knows.