systemicrisk (version 0.4.2)

Model.p.Fitness.Servedio: Multiplicative Fitness Model for Power Law

Description

This model has a power law of the degree distribution with a parameter \(\alpha\) and is tuned to a desired link existence probability. It is based on a fitness model.

Usage

Model.p.Fitness.Servedio(n, alpha, meandegree, sdprop = 0.1)

Arguments

n

dimension of matrix.

alpha

exponent for power law. Must be <=-1.

meandegree

overall mean degree (expected degree divided by number of nodes). Must be in (0,1).

sdprop

standard deviation of updated steps.

Details

Every node \(i\) has a fitness \(\theta_i\) being an independent realisation of a U[0,1] distribution. The probability of a link between a node with fitness x and a node with fitness y is g(x)g(y) where g is as follows. If \(\alpha=-1\) then $$g(x)=g0*\exp(-\log(g0)*x)$$ Otherwise, $$g(x)=(g0^(\alpha+1)+(1-g0^(\alpha+1))*x)^(1/(\alpha+1))$$ where \(g0\) is tuned numerically to achieve the desired overall mean degree.

Updating of the model parameters in the MCMC setup is done via a Metropolis-Hastings step, adding independent centered normal random variables to each node fitness in \(\theta\).

References

Servedio V. D. P. and Caldarelli G. and Butta P. (2004) Vertex intrinsic fitness: How to produce arbitrary scale-free networks. Physical Review E 70, 056126.

Examples

# NOT RUN {
n <- 5
mf <- Model.p.Fitness.Servedio(n=n,alpha=-2.5,meandegree=0.5)
m <- Model.Indep.p.lambda(model.p=mf,
                          model.lambda=Model.lambda.GammaPrior(n,scale=1e-1))
x <- genL(m)
l <- rowSums(x$L)
a <- colSums(x$L)
res <- sample_HierarchicalModel(l,a,model=m,nsamples=10,thin=10)


# }