The theory of Smax graph does not seem to work in a real case study

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)401-412
Journal / PublicationDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Issue number3-4
Publication statusPublished - Jun 2006


A recent study has shown that the power-law degree distribution alone may not guarantee a network be scale-free. Meanwhile, a structural metric was formulated to represent the extent to which a network is scale-free, where a new concept of smax graph was suggested, associated with a measure of a network being fully scale-free. Following this approach, in our recent investigation of a real competitive relationship network of enterprises in the software industry in Guangzhou city, China, we constructed and analyzed the smax graph of the real network, hoping that this case study could help us confirm the seemingly attractive new theory. It turns out, however, that the concept of smax graph does not preserve many essential features of the real network. To that end, the main reason for the failure of the original concept of smax graph is discussed, with a possible remedy suggested for future research. Copyright © 2006 Watam Press.

Research Area(s)

  • Competitive relationship network, Power-law distribution, Smax graph, Scale-free network