Classes of Small-World Networks

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 97; no. 21; pp. 11149 - 11152
• Main Authors: Amaral, L. A. N., Scala, A., Barthelemy, M., Stanley, H. E.
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences of the United States of America 10.10.2000; National Acad Sciences; National Academy of Sciences; The National Academy of Sciences
• Subjects: Airports; Church of Jesus Christ of Latter Day Saints; Connectivity; Friendship; Interpersonal Relations; Mathematical models; Nerve Net; Neurons; Nonlinear Dynamics; Passengers; Physical Sciences; Polymers; Power laws; Social networking; Statistical analysis; Vertices
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.200327197

We study the statistical properties of a variety of diverse real-world networks. 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, characterized by a connectivity distribution that has a power law regime followed by a sharp cutoff; and (c) single-scale networks, characterized by a connectivity distribution with a fast decaying tail. Moreover, we note for the classes of broad-scale and single-scale networks that there are constraints limiting the addition of new links. Our results suggest that the nature of such constraints may be the controlling factor for the emergence of different classes of networks.