c03_netw_prop_handout - Properties of real networks: degree...

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1 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. semilog 10 0 10 1 10 2 10 3 10 -3 10 -2 10 -1 10 0 .5 1 20 40 60 80 100 0.2 0.6 1 linear Plotting power laws and exponentials Note: these are plots of functions and not degree distributions 10 -4 loglog 1 cx ) x ( f = x c ) x ( f = 5 0 . cx ) x ( f = In- and out-degree distribution of the WWW 1 2 45 2 . . ) ( ) ( k k P k k P in out nodes: webpages edges: hyperlinks R. Albert, H. Jeong, A.-L. Barabási, Nature 401, 130 (1999) A. Broder et al ., Comput. Netw. 33, 309 (1999) Usage: the degree distribution scales as a power law Degree distributions in networks of science collaborations Coauthor, neurosci. Coauthor, HEP ) ( k P 2 1 . ) ( k k P 1 2 . ) ( k 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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2 Power-law degree distributions were found in diverse networks Actor collaboration Internet, router level ) ( k P nodes: routers edges: cables nodes: actors edges: cast jointly 3 31 + ) k ( ) k ( P 4 2 . ) ( k k P A.-L. Barabási, R. Albert, Science 286, 509 (1999) R. Govindan, H. Tangmunarunkit, IEEE Infocom (2000) k 1 10 2 10 1 10 3 10 2 10 3 10 0 10
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c03_netw_prop_handout - Properties of real networks: degree...

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