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

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 s_max 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 s_max 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 s_max 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 s_max graph is discussed, with a possible remedy suggested for future research. Copyright © 2006 Watam Press.