Numeric scalar, the power law exponent of the degree
distribution. For directed graphs, this specifies the exponent of the
out-degree distribution. It must be greater than or equal to 2. If you pass
Inf here, you will get back an Erdos-Renyi random network.
exponent.in
Numeric scalar. If negative, the generated graph will be
undirected. If greater than or equal to 2, this argument specifies the
exponent of the in-degree distribution. If non-negative but less than 2, an
error will be generated.
loops
Logical scalar, whether to allow loop edges in the generated
graph.
multiple
Logical scalar, whether to allow multiple edges in the
generated graph.
finite.size.correction
Logical scalar, whether to use the proposed
finite size correction of Cho et al., see references below.
Details
This game generates a directed or undirected random graph where the degrees
of vertices follow power-law distributions with prescribed exponents. For
directed graphs, the exponents of the in- and out-degree distributions may
be specified separately.
The game simply uses sample_fitness 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 sample_fitness 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+i0-1)^(-alpha) where i0 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.