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NARVAL_T_Waxman

Generate a random network topology in respect with the Waxman algorithm.

Calling Sequence

[g,d] = NARVAL_T_Waxman(a,b,n,l)

Parameters

a :

first parameter of the Waxman model.

b :

second parameter of the Waxman model.

n :

network size.

l :

network squared area side.

g :

network graph.

d :

node degree distribution.

Description

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.

Examples

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');

Dependency

NARVAL_F_XYRand, NARVAL_F_Distance, NARVAL_G_MakeGraph, NARVAL_G_EdgeLength

Authors

Foued Melakessou

Contact

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

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