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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/games.R
\name{sample_fitness}
\alias{sample_fitness}
\alias{static.fitness.game}
\title{Random graphs from vertex fitness scores}
\usage{
sample_fitness(no.of.edges, fitness.out, fitness.in = NULL,
loops = FALSE, multiple = FALSE)
}
\arguments{
\item{no.of.edges}{The number of edges in the generated graph.}
\item{fitness.out}{A numeric vector containing the fitness of each vertex.
For directed graphs, this specifies the out-fitness of each vertex.}
\item{fitness.in}{If \code{NULL} (the default), the generated graph will be
undirected. If not \code{NULL}, then it should be a numeric vector and it
specifies the in-fitness of each vertex.
If this argument is not \code{NULL}, then a directed graph is generated,
otherwise an undirected one.}
\item{loops}{Logical scalar, whether to allow loop edges in the graph.}
\item{multiple}{Logical scalar, whether to allow multiple edges in the
graph.}
}
\value{
An igraph graph, directed or undirected.
}
\description{
This function generates a non-growing random graph with edge probabilities
proportional to node fitness scores.
}
\details{
This game generates a directed or undirected random graph where the
probability of an edge between vertices \eqn{i} and \eqn{j} depends on the
fitness scores of the two vertices involved. For undirected graphs, each
vertex has a single fitness score. For directed graphs, each vertex has an
out- and an in-fitness, and the probability of an edge from \eqn{i} to
\eqn{j} depends on the out-fitness of vertex \eqn{i} and the in-fitness of
vertex \eqn{j}.
The generation process goes as follows. We start from \eqn{N} disconnected
nodes (where \eqn{N} is given by the length of the fitness vector). Then we
randomly select two vertices \eqn{i} and \eqn{j}, with probabilities
proportional to their fitnesses. (When the generated graph is directed,
\eqn{i} is selected according to the out-fitnesses and \eqn{j} is selected
according to the in-fitnesses). If the vertices are not connected yet (or if
multiple edges are allowed), we connect them; otherwise we select a new
pair. This is repeated until the desired number of links are created.
It can be shown that the \emph{expected} degree of each vertex will be
proportional to its fitness, although the actual, observed degree will not
be. If you need to generate a graph with an exact degree sequence, consider
\code{\link{sample_degseq}} instead.
This model is commonly used to generate static scale-free networks. To
achieve this, you have to draw the fitness scores from the desired power-law
distribution. Alternatively, you may use \code{\link{sample_fitness_pl}}
which generates the fitnesses for you with a given exponent.
}
\examples{
N <- 10000
g <- sample_fitness(5*N, sample((1:50)^-2, N, replace=TRUE))
degree_distribution(g)
\dontrun{plot(degree_distribution(g, cumulative=TRUE), log="xy")}
}
\references{
Goh K-I, Kahng B, Kim D: Universal behaviour of load
distribution in scale-free networks. \emph{Phys Rev Lett} 87(27):278701,
2001.
}
\author{
Tamas Nepusz \email{ntamas@gmail.com}
}
\keyword{graphs}
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