TY - GEN
T1 - A small-world model of scale-free networks
T2 - International Conference on Intelligent Structure and Vibration Control, ISVC 2011
AU - Xiao, Wenjun
AU - Jiang, Shizhong
AU - Chen, Guanrong
PY - 2011
Y1 - 2011
N2 - It is now well known that many large-sized complex networks obey a scale-free powerlaw vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent γ ≥ 2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of k 1 γ , k 2 γ, . . ., k l γ, and l is less than log N, where l = k 1 2 <⋯ l is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks. © (2011) Trans Tech Publications.
AB - It is now well known that many large-sized complex networks obey a scale-free powerlaw vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent γ ≥ 2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of k 1 γ , k 2 γ, . . ., k l γ, and l is less than log N, where l = k 1 2 <⋯ l is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks. © (2011) Trans Tech Publications.
KW - Complex network
KW - Computer network
KW - Scale-free network
KW - Small-world network
KW - Software network
UR - http://www.scopus.com/inward/record.url?scp=79951623385&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-79951623385&origin=recordpage
U2 - 10.4028/www.scientific.net/AMM.50-51.166
DO - 10.4028/www.scientific.net/AMM.50-51.166
M3 - RGC 32 - Refereed conference paper (with host publication)
SN - 9783037850206
VL - 50-51
T3 - Applied Mechanics and Materials
SP - 166
EP - 170
BT - Intelligent Structure and Vibration Control
Y2 - 14 January 2011 through 16 January 2011
ER -