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Phys Rev Lett. 2001 Dec 31;87(27 Pt 1):278701. Epub 2001 Dec 12.

Universal behavior of load distribution in scale-free networks.

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School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea.


We study a problem of data packet transport in scale-free networks whose degree distribution follows a power law with the exponent gamma. Load, or "betweenness centrality," of a vertex is the accumulated total number of data packets passing through that vertex when every pair of vertices sends and receives a data packet along the shortest path connecting the pair. It is found that the load distribution follows a power law with the exponent delta approximately 2.2(1), insensitive to different values of gamma in the range, 2 < gamma < or = 3, and different mean degrees, which is valid for both undirected and directed cases. Thus, we conjecture that the load exponent is a universal quantity to characterize scale-free networks.

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