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NL_T_WaxmanConnexHD

Generate a random hierarchic network topology of nodes linearly distributed into layers in respect with the Waxman model.

Calling Sequence

[G,D,V] = NL_T_WaxmanConnexHD(A,B,N,L,Nl,S,Db,Dd,C)

Arguments

A :

First parameter of the Waxman model.

B :

Second parameter of the Waxman model.

N :

Network size.

L :

Network squared area side.

:

Maximal quantity of nodes per subnetwork.

S :

Quantity of network layers.

:

Original diameter of nodes.

:

Diameter difference between successive network layers.

C :

Color of each network layer.

G :

Graph.

D :

Diameter of each network node.

V :

Quantity of nodes per network layer.

Description

NL_T_WaxmanConnexHD generates the random hierarchic network topology G of size N.

The quantity of nodes per layer is determined by a linear distribution. The first layers have fewer nodes than the latest ones. The network backbone 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 backbone needs to be fully connected. Thereafter S-1 layers are added according 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. C, and are only used to emphasize the hierarchical structure of the generated network. C is a S-length vector that contains the colors used to display each network layer. The nodes of the first layer have a diameter equal to . The nodes diameter is constant for a layer, but we reduce to its current value when we move to the next layer. For instance, if the starting diameter is 20 for the network backbone, nodes of the layer 2 will have a diameter of 15 if 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=100;//network 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]=NL_T_WaxmanConnexHD(a,b,n,l,nl,s,db,dd,cv);//application of NL_T_WaxmanConnexHD
ind=1;//window index
f=NL_G_ShowGraph(g,ind);//graph visualization

Dependency

NL_T_WaxmanConnexC, NL_T_AddWaxman2Node, NL_G_Star, NL_G_GraphEdgesLength

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