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NARVAL_T_HierWaxmanCon

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

Calling Sequence

[g,d,v] = NARVAL_T_HierWaxmanCon(a,b,n,l,nl,s,db,dd,cv)

Parameters

a :

first parameter of the Waxman model.

b :

second parameter of the Waxman model.

n :

network backbone size.

l :

network squared area side.

nl :

maximal quantity of nodes per subnetwork.

s :

quantity of network layers.

db :

original diameter of nodes.

dd :

diameter difference between successive network layers.

cv :

color of each network layer.

g :

network graph.

d :

diameter of each network node.

v :

quantity of nodes per network layer.

Description

NARVAL_T_HierWaxmanCon generates the random hierarchic network topology g.

The network backbone of size n is assumed to be created in respect with the Waxman algorithm of parameters a and b. The largest connex subnetwork is extracted. As a matter of course the topology of the backbone needs to be fully connected. Thereafter s-1 layers are added according to the Waxman algorithm (the same parameters a and b are used for each network layer). New nodes are added by small groups of size randomly selected into the range [1 2 3 4 ... nl]. Finally basic users (1-degree) are linked to the last network layer. cv, db and dd are only used to emphasize the hierarchic structure of the generated network. cv is a s-length vector that contains the colors used to display each layer. The nodes of the first layer have a diameter equal to db. The nodes diameter is constant for a layer, but we reduce dd to its current value when we move to the next layer. For instance, if the starting node diameter is 20 for the network backbone, nodes of the layer 2 will have a diameter of 15 if dd rates 5. d finally provides the diameter of each network node. v gathers the quantity of nodes per network layer.

Examples

a=0.3;//first parameter of the Waxman model
b=0.4;//second parameter of the Waxman model
n=30;//network backbone size
l=1000;//network squared area side
nl=5;//maximal quantity of nodes per subnetwork
s=2;//quantity of network layers
db=20;//original diameter of nodes
dd=5;//diameter difference between successive network layers
cv=[2 5 6 1];//color of each network layer
[g,d,v]=NARVAL_T_HierWaxmanCon(a,b,n,l,nl,s,db,dd,cv);//application of NARVAL_T_HierWaxmanCon
ind=1;//window index
f=NARVAL_G_ShowGraph(g,ind);//graph visualization

Dependency

NARVAL_T_WaxmanConnex2, NARVAL_G_WCirclePlace, NARVAL_G_CirclePlace, 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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