Zipf, Power-laws, and Pareto - a ranking tutorial

Zipf, Power-laws, and Pareto - a ranking tutorial is a handy paper by Lada Adamic which clearly and briefly explains how to grok these concepts. This tutorial is very useful if you need to compute the exponent of the power law distribution of degrees that is often found in social networks.

Abstract
Many man made and naturally occurring phenomena, including city sizes, incomes, word frequencies, and earthquake magnitudes, are distributed according to a power-law distribution. A power-law implies that small occurrences are extremely common, whereas large instances are extremely rare. This regularity or 'law' is sometimes also referred to as Zipf and sometimes Pareto. To add to the confusion, the laws alternately refer to ranked and unranked distributions. Here we show that all three terms, Zipf, power-law, and Pareto, can refer to the same thing, and how to easily move from the ranked to the unranked distributions and relate their exponents.