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NARVAL >> NL_T: Topology > NL_T_Waxman

NL_T_Waxman

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

Calling Sequence

[G,D] = NL_T_Waxman(A,B,N,L)

Arguments

A :

First parameter of the Waxman model.

B :

Second parameter of the Waxman model.

N :

Graph size.

L :

Network squared area side.

G :

Graph.

D :

Node degree distribution.

Description

NL_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 . 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]=NL_T_Waxman(a,b,n,l);//application of NL_T_Waxman
ind=1;//window index
f=NL_G_ShowGraphN(g,ind);//graph visualization
i2=2;//window index
scf(i2);
clf(i2);
plot(d);
plot2d3(d);//graph visualization
xtitle('','node index','degree');

Dependency

NL_F_RandVectorCoord, NL_F_DistanceNiNj, NL_G_MakeGraph, NL_G_GraphEdgesLength

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