Measure for characterizing heavy-tailed networks

Abstract

The phrase "scale-free network"has become controversial in recent years, as network scientists debate what it means for a finite degree sequence to fit a power-law distribution. In practical terms, however, most network scientists use the phrase to indicate that a network has hubs, and so it would be useful to be able to talk about such networks without reference to power laws at all. This paper presents the Cooke-Nieboer index (CNI), a nonasymptotic measure of the heavy-tailedness of a network's empirical degree distribution which does not presume a power-law form. The CNI is easy to calculate and is able to distinguish between synthetic networks with power-law, exponential, and symmetric degree distributions. It serves as a complementary measure to the traditional tail-index estimators and reflects certain properties in real-life networks better than the estimators do.