 On necessary conditions for scale-freedom in complex networks, with applications to computer communication systemsW.J. Xiao, W.D. Chen and B. Parhami International Journal of Systems Science, 2011, vol. 42, issue 6, 951-958 Abstract: Many complex networks exhibit a scale-free, power-law distribution of vertex degrees. This common feature is a consequence of two generic mechanisms relating to the formation of real networks: (i) networks tend to expand over time through the addition of new vertices and (ii) new vertices attach preferentially to those that are already well connected. We show that for many natural or man-made complex networks possessing a scale-free power-law distribution with the exponent γ ≥ 2, the number of degree-1 vertices, when nonzero, is of the same order as the network size N and that the average degree is of order at most log N. Our results expose another necessary characteristic of such networks. Furthermore, our method has the benefit of relying only on conditions that are static and easily verified for arbitrary networks. We use the preceding results to derive a closed-form formula approximating the distance distribution in scale-free networks. Such distributions are applied extensively in the fields of computer communication and software architecture, among other domains. Date: 2011 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:tsysxx:v:42:y:2011:i:6:p:951-958 Ordering information: This journal article can be ordered from DOI: 10.1080/00207720903267841 Access Statistics for this article International Journal of Systems Science is currently edited by Visakan Kadirkamanathan More articles in International Journal of Systems Science from Taylor & Francis Journals |
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