static.power.law.game (no.of.nodes, no.of.edges, exponent.out,
exponent.in = -1, loops = FALSE,
multiple = FALSE, finite.size.correction = TRUE)
Inf
here, you will get back an
The game simply uses static.fitness.game
with appropriately
constructed fitness vectors. In particular, the fitness of vertex
$i$ is $i^{-alpha}$, where $alpha = 1/(gamma-1)$
and gamma is the exponent given in the arguments.
To remove correlations between in- and out-degrees in case of directed
graphs, the in-fitness vector will be shuffled after it has been set up
and before static.fitness.game
is called.
Note that significant finite size effects may be observed for exponents smaller than 3 in the original formulation of the game. This function provides an argument that lets you remove the finite size effects by assuming that the fitness of vertex $i$ is $(i+i_0-1)^{-alpha}$ where $i_0$ is a constant chosen appropriately to ensure that the maximum degree is less than the square root of the number of edges times the average degree; see the paper of Chung and Lu, and Cho et al for more details.
Chung F and Lu L: Connected components in a random graph with given degree sequences. Annals of Combinatorics 6, 125-145, 2002.
Cho YS, Kim JS, Park J, Kahng B, Kim D: Percolation transitions in scale-free networks under the Achlioptas process. Phys Rev Lett 103:135702, 2009.
g <- static.power.law.game(10000, 30000, 2.2, 2.3)
plot(degree.distribution(g, cumulative=TRUE, mode="out"), log="xy")
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