Generate a random network topology in respect with the Waxman algorithm.
[G,D] = NL_T_Waxman(A,B,N,L)
First parameter of the Waxman model.
Second parameter of the Waxman model.
Graph size.
Network squared area side.
Graph.
Node degree distribution.
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.
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'); | ![]() | ![]() |