Generate a random connex network topology in respect with the Waxman model.
[g] = NARVAL_T_WaxmanConnex(a,b,n,l)
first parameter of the Waxman model.
second parameter of the Waxman model.
network size.
network squared area side.
network graph.
NARVAL_T_WaxmanConnex 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 p(d)=α*e^(-d/(β*l). 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. The largest connex component of the generated graph is extracted.
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