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 the 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 the two nodes u and v is given by p(d)=α*e^(-d/(β*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. The two parameters α and β are needed in order to entirely define WM. If α and β belong to [0,1], then p(d) is also included into the range [0,1]. When α increases, the amount of links grows too. The ratio between the quantity of long and short links changes in the same manner than β 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). The 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;//window index f=NARVAL_G_ShowNodesIndex(g,ind);//graph visualization i2=2;//window index scf(i2); clf(i2); plot(d); plot2d3(d);//graph visualization xtitle('','node index','degree'); | ![]() | ![]() |
Dr. Foued Melakessou
Research Associate
Interdisciplinary Centre for Security, Reliability and Trust
Room F106
University of Luxembourg
6, rue Coudenhove Kalergi
L-1359 Luxembourg-Kirchberg
E-mail: foued.melakessou@uni.lu
Tel: (+352) 46 66 44 5346