A measure for characterizing heavy-tailed networks

Heavy-tailed networks are often characterized in the literature by their degree distribution's similarity to a power law. However, many heavy-tailed networks in real life do not have power-law degree distributions, and in many applications the scale-free nature of the network is irrelevant so long as the network possesses hubs. Here we present the Cooke-Nieboer index (CNI), a non-asymptotic measure of the heavy-tailedness of a network's degree distribution which does not presume a power-law form. The CNI is easy to calculate, and clearly distinguishes between networks with power-law, exponential, and symmetric degree distributions.