Fundamental Structural Constraint of Random Scale-Free Networks

Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea.
Physical Review Letters (Impact Factor: 7.51). 07/2012; 109(11). DOI: 10.1103/PhysRevLett.109.118701
Source: arXiv


We study the structural constraint of random scale-free networks that
determines possible combinations of the degree exponent $\gamma$ and the upper
cutoff $k_c$ in the thermodynamic limit. We employ the framework of
graphicality transitions proposed by [Del Genio and co-workers, Phys. Rev.
Lett. {\bf 107}, 178701 (2011)], while making it more rigorous and applicable
to general values of kc. Using the graphicality criterion, we show that the
upper cutoff must be lower than $k_c N^{1/\gamma}$ for $\gamma < 2$, whereas
any upper cutoff is allowed for $\gamma > 2$. This result is also numerically
verified by both the random and deterministic sampling of degree sequences.

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Available from: Meesoon Ha, Feb 12, 2014

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