brainwaver (version 1.6)

equadist.rand.sw: Small-world parameters for a simulated graph given its degree distribution

Description

Computes the degree, the minimum path length and the clustering coefficient for a simulated graph with a known degree distribution.

Usage

equadist.rand.sw(nsim, dat = "reduced", dist.mat, degree.dist)

Arguments

nsim

number of simulated graphs to use for the computation of the small-world parameters.

dat

character string specifying if all the small-world parameters have to be returned. If "reduced", only the mean of the parameters for the whole graph is returned.

dist.mat

matrix with a distance associated to each pair of nodes of the graph to take into account in the computation of the small-world parameters.

degree.dist

vector describing the degree distribution verified by the nodes of the simulated graph.

Value

in.degree

mean of the degree for the whole graph.

Lp.rand

mean of the minimum path length for the whole graph.

Cp.rand

mean of the clustering coefficient for the whole graph.

in.degree.all

vector of the degree of each node of the graph.

Lp.rand.all

vector of the minimum path length of each node of the graph.

Cp.rand.all

vector of the clustering coefficient of each node of the graph.

Details

Because of the problem for the simulation of a random graph with exactly the same degree distribution, each simulation applied in this function is subject to the result to get a graph with the same number of edges as expected. So, the number of wanted simulations can be very different from the number of simulations taken into account in the computation of the small-world parameters.

References

S. H. Strogatz (2001) Exploring complex networks. Nature, Vol. 410, pages 268-276.

S. Achard, R. Salvador, B. Whitcher, J. Suckling, Ed Bullmore (2006) A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs. Journal of Neuroscience, Vol. 26, N. 1, pages 63-72.

See Also

sim.equadist, rand.sw, reg.sw

Examples

#For a scale-free graph

x<-1:50
probx<-x^(-1.4)
n.nodes<-50
n.edges<-250

stop<-0

while(stop==0){
write.table(stop)
r<-sample(x,n.nodes,prob=probx,replace=TRUE)
if(sum(r)==n.edges) stop<-1
  }

sf.degree<-r

mat<-sim.equadist(sf.degree)

result<-equadist.rand.sw(10, dat = "reduced", dist.mat=matrix(1,50,50), 
	                  degree.dist=sf.degree)