These "rich-getting-richer" addresses may actually be held by businesses, and the reason they are gaining more links and BTC is because more people are storing their BTC with that business.
The study doesn't provide nearly enough evidence or context to justify MIT Tech Review's politically-loaded rhetoric. There are ways to report on the Bitcoin network without mucking it up with divisive classist rhetoric.
In an inflationary world, the rich actually get poorer, but typically have the means to invest and thus negate the inflationary loss...
The reason for the typical rich-get richer scenario in the real world is that the rich have enough assets that they don need to be liquid that they can invest and increase their wealth, whereas the poor need to keep their assets liquid for potential hard times, and thus by not investing they lose value to inflation.
It's actually very difficult to make bitcoins with bitcoin investment, there's only risky bets and day trading right now. There are no reliable interest-bearing instruments.
And of course this is true. For any given node in an example network, the number of incoming links to it is the same as the number of people who have already 'vouched' for that person. Obviously, more links are given to those who already have higher credibility in virtue of being vouched for. In a social network this is true and in an economy this is true. The more incoming links you have, the stronger your 'brand,' the more incoming links you have.
More than just a currency, what BitCoin offers is the most complete data on any economy. In no other economy is a complete record of every transaction, and every amount of every transaction, available. I wouldn't be surprised if BitCoin's economy becomes an extremely popular laboratory for academic economists to study actual, real-life economic effects with great precision.
Naturally, those who engage in many transactions initially are likely to engage in even more transactions in the future (ex. a new exchange starts with many transactions and gets even more over time). This has no correlation with actual wealth.
If we were to apply this logic to the real world, one would reach the startling conclusion that delis are wealthier than high fashion boutiques.
So if this is some way represented the real economy, it would be saying that in a given month, some people get 1000 times richer, some get 1000 times poorer, but in some average sense, the rich tend to get slightly richer.
The whole article has the feel of researchers taking the data that exists and is easy to analyze, doing some simple computations that are completely meaningless, and then pretending these computations have some implications for society.
EDIT: I was mis-reading that graph, but the point remains that bitcoin accounts are no a meaningful quantity (if we are interested in the wealth of individuals). In particular that figure (and their observations that the rate of growth is higher for higher balances) only applies to the subset of accounts whose balance increases. When you look at the accounts whose balance decreases, almost all of the time the balance goes to zero.
Rather it's human behaviour which determines wealth and distribution of wealth. So while this effect is certainly something that economists study and will continue to study, it's entirely due to human behaviour, independent of the 'type' of economy. Even in Communist countries you see this effect - the ruling party consolidate their wealth and power while the subjects are handed out a finite amount of resources/wealth.
Science does not spent time on fantasy. Science is for things that exist in the observable world.
Now if you'll excuse me, I'm off to go work on my Turing machine with infinite memory and all that jazz...
Economics is as much theory as it is observation. Much like other sciences, for example, math and physics.
An economic system with the controls in place to stop the Matthew effect would look nothing like a free market.