Generate a random network topology in respect with the Waxman algorithm.
[g,d]=NARVAL_T_Waxman(a,b,n,l)
first parameter of the Waxman model.
second parameter of the Waxman model.
network size.
network squared area side.
network graph.
node degree distribution.
NARVAL_T_Waxman generates a random network topology g in respect with the Waxman algorithm. The Waxman Method (WM) stays the most used model as it provides an accurate representation for real networks at least at the geographic level. A random graph of n nodes uniformly distributed inside a square is generated. The probability p to connect two nodes u and v is given by p(d)=alpha*e^(-d/(b*l). d corresponds to the Euclidean distance between u and v. l is the maximal distance between two random nodes. Generally it rates the network square side where nodes are placed. Two parameters a and b are needed in order to entirely define WM. If a and b belong to [0,1], then p(d) is also included into the range [0,1]. When a increases, the amount of links grows too. The ratio between the quantity of long and short links changes in the same manner than b does. Network edges are attributed as what follows. For each set of two distinct network nodes u and v, the distance d between u and v is performed, then p(d) is calculated for the set (u,v). A random value t is generated according to a uniform distribution in [0,1]. If t is inferior to p(d), a link is created between u and v.
a=0.1;//first parameter of the Waxman model b=0.8;//second parameter of the Waxman model n=100;//network size l=1000;//network squared area side [g,d]=NARVAL_T_Waxman(a,b,n,l);//application of NARVAL_T_Waxman ind=1; f=NARVAL_G_ShowGraph(g,ind); i2=2; scf(i2); clf(i2); plot(d); plot2d3(d); xtitle('','node index','degree'); | ![]() | ![]() |