Throughout many fields of science, one finds quantities which behave (or are claimed to behave) according to a *power-law distribution.* That is, one quantity of interest, *y,* scales as another number *x* raised to some exponent:

[tex] y \propto x^{-\alpha}.[/tex]

Power-law distributions made it big in complex systems when it was discovered (or rather re-discovered) that a simple procedure for growing a network, called “preferential attachment,” yields networks in which the probability of finding a node with exactly *k* other nodes connected to it falls off as *k* to some exponent:

[tex]p(k) \propto k^{-\gamma}.[/tex]

The constant γ is typically found to be between 2 and 3. Now, from my parenthetical remarks, the Gentle Reader may have gathered that the story is not quite a simple one. There are, indeed, many complications and subtleties, one of which is an issue which might sound straightforward: how do we know a power-law distribution when we see one? Can we just plot our data on a log-log graph and see if it falls on a straight line? Well, as Eric and I are fond of saying, “You can hide a multitude of sins on a log-log graph.”

Via Dave Bacon comes word of a review article on this very subject. Clauset, Shalizi and Newman offer us “Power-law distributions in empirical data” (7 June 2007), whose abstract reads as follows:

Continue reading Power-law Distributions in Empirical Data →