c03_netw_prop

c03_netw_prop - Properties of real networks: degree di...

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Properties of real networks: degree distribution Nodes with small degrees are most frequent. The fraction of highly connected nodes decreases, but is not zero. Look closer: use a logarithmic plot.
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10 0 10 1 10 2 10 3 0 0 10 -1 10 .5 10 -2 semilog 10 -3 glog 1 1 Plotting power laws nd exponentials 10 -4 loglog 0.6 linear and exponentials Note: these are plots of nctions and not degree 1 cx ) x ( f = 5 0 . cx ) x ( f = 20 40 60 80 100 0.2 functions and not degree distributions x c ) x ( f =
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In- and out-degree distribution of the WWW nodes: webpages edges: hyperlinks 45 2 . ) ( k k P out 1 2 . ) ( k k P in Usage: the degree distribution scales as a power law R. Albert, H. Jeong, A.-L. Barabási, Nature 401, 130 (1999) A. Broder et al ., Comput. Netw. 33, 309 (1999)
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Degree distributions in networks of science ollaborations collaborations Coauthor, neurosci. Coauthor, HEP 2 1 . ) ( k k P 1 2 . ) ( k k P ) ( k P M. E. J. Newman, Phys. Rev. E 64, 016131 (2001) A.-L. Barabási et al., cond-mat/0104162 (2001)
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Power-law degree distributions were found in iverse networks diverse networks Actor collaboration Internet, router level odes: actors nodes: routers edges: cables nodes: actors edges: cast jointly 3 31 + ) k ( ) k ( P 4 2 . ) ( k P ) ( k k P R. Govindan, H. Tangmunarunkit, IEEE Infocom (2000) k 1 10 2 10 1 10 3 10 2 10 3 10 0 10 A.-L. Barabási, R. Albert, Science 286, 509 (1999)
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c03_netw_prop - Properties of real networks: degree di...

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