Classes of small-world networks

We study the statistical properties of a variety of diverse real-world netw orks. We present evidence of the occurrence of three classes of small-world networks: (a) scale-free networks, characterized by a vertex connectivity distribution that decays as a power law; (b) broad-scale networks, characte rized by a connectivity distribution that has a power law regime followed b y a sharp cutoff; and (c) single-scale networks, characterized by a connect ivity distribution with a fast decaying tail. Moreover. we note for the cla sses of broad-scale and single-scale networks that there are constraints li miting the addition of new links. Our results suggest that the nature of su ch constraints may be the controlling factor for the emergence of different classes of networks.