Fairness on the web: alternatives to the power law

This paper presents several measures of fairness and inequality based on the degree distribution in networks, as alternatives to the well-established power-law exponent. Networks such as social networks, communication networks and the World Wide Web itself are often characterized by their unequal distribution of edges: Few nodes are attached to many edges, while many nodes are attached to only few edges. The inequality of such network structures is typically measured using the power-law exponent, stating that the number of nodes with a given degree is proportional to that degree taken to a certain exponent. However, this approach has several weaknesses, such as its narrow applicability and expensive computational complexity. Beyond the fact that power laws are by far not a universal phenomenon on the Web, the power-law exponent has the surprising property of being negatively correlated with the usual notion of inequality, making it unintuitive as a fairness measure. As alternatives, we propose several measures based on the Lorenz curve, which is used in economics but rarely in networks study, and on the information-theoretical concept of entropy. We show in experiments on a large collection of online networks that these measures do not suffer under the drawbacks of the power-law exponent.