<< NL_T_LocalityNodeRange NL_T: Topology NL_T_NewLayerWaxman >>

NARVAL >> NL_T: Topology > NL_T_MultiLevel

NL_T_MultiLevel

Generate a random hierarchic network based on successive layers generated by the Waxman algorithm.

Calling Sequence

[G,D,Nl] = NL_T_MultiLevel(A,B,Nl,L,N,S,B,E,C)

Arguments

A :

First parameter of the Waxman model for each network layer.

B :

Second parameter of the Waxman model for each network layer.

:

Quantity of nodes per network layer.

L :

Squared area side per network layer.

N :

Maximal quantity of nodes per subnetwork for each layer.

S :

Quantity of network layers.

B :

Original diameter of nodes.

E :

Diameter difference between successive network layers.

C :

Color of each network layer.

G :

Graph.

D :

Diameter of each network node.

Description

NL_T_MultiLevel generates the random hierarchic network G composed by S layers.

We want to attribute nodes into the first layer, nodes into the second layer and so on. Each subnetwork is generated in respect with the Waxman algorithm. Users must enter the three vectors A, B and L having the same size than Nl. A (respectively B) clusters the α (respectively β) parameters used by the Waxman algorithm in order to generate subnetworks for each layer. L gathers the square area side values needed for the calculation of probabilities. Then A(i) and B(i) are the Waxman parameters of the network layer i. L(i) is the subnetwork square side at the layer i. In respect with our modeling, the first layer corresponds to the network backbone. For this layer, we use the Connex Waxman Algorithm. C, B and E 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 B. The nodes diameter is constant for a layer, but we reduce E 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 E rates 5.

For the layer level i from 2 to S-1, the placement of nodes is done as what follows. We suppose that the composition of the previous layer i-1 is known. Let Li be the quantity of nodes belonging to the layer i. We initialize the vector P containing all nodes of the layer i-1. We want to place N(i) nodes on this layer. In order to fairly attribute nodes around each subnetwork of the previous layer, we suggest to place nodes per small groups in respect with the vector n. Then for the layer 2 with N(2), we randomly place subnetworks of k nodes selected from the uniform distribution [ 1 2 3 4 ... Nm] around the node Nc of the layer i-1 randomly selected into the vector P (in this case ). After each iterative process, Nc is removed from P in order to fairly attribute subnetworks to the nodes of the layer i-1. When P becomes empty, we reinitialize it with its original value. Finally if the quantity of desired nodes for a layer has not been reached, we translate the difference to the latest layer.

Examples

a=[0.3 0.3 0.3 0.3];//first parameter of the Waxman model for each network layer
b=[0.9 0.7 0.5 0.3];//second parameter of the Waxman model for each network layer
nl=[30 50 50 100];//quantity of nodes per network layer
l=[1000 150 100 40];//squared area side per network layer
n=[3 5 3 3];//maximal quantity of nodes per subnetwork for each layer
s=4;//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,nl]=NL_T_MultiLevel(a,b,nl,l,n,s,db,dd,cv);//application of NL_T_MultiLevel
ind=1;//window index
f=NL_G_ShowGraph(g,ind);//graph visualization

Dependency

NL_T_WaxmanConnexC, NL_T_NewLayerWaxman, NL_F_RandVectorNoRepl, NL_G_Star, NL_G_GraphEdgesLength

Report an issue
<< NL_T_LocalityNodeRange NL_T: Topology NL_T_NewLayerWaxman >>