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NARVAL_T_BarabasiAlbert

Generate a random topology in respect with the Barabasi-Albert model.

Calling Sequence

[g,d] = NARVAL_T_BarabasiAlbert(n,l,L)

Parameters

n :

network size.

l :

threshold of new links created at each network growth.

L :

network square area side.

g :

network graph.

d :

vector of each node degree.

Description

NARVAL_T_BarabasiAlbert generates the random topology g composed by n nodes randomly placed inside the square area of side L in respect with the Barabasi-Albert model (WIKIPEDIA). The vector d gathers the node degree of each topology element. Thus its first value corresponds to the node degree of the first node, its second value to the node degree of the second node and so on. Two important general concepts are included in the Barabasi-Albert model: Growth and Preferential Attachment. In fact both concepts widely exist in real networks: Growth means that the quantity of nodes included into the network increases over time and Preferential Attachment signifies that the more connected a node is, the more likely it is to receive new links. Thus nodes with the highest degree present a stronger ability to grab new links freshly added to the network. For instance new pages on the web link preferentially to very well-known sites such as Google or Wikipedia. Preferential Attachment consists of a positive feedback cycle where initial random changes are systematically reinforced. Consequently this phenomenon greatly magnifies differences. Then a node initially having more links or having started accumulating links earlier than another node will become a network hub. The network begins with an initial network of m nodes. m should be greater or equal to 2 in order to generate fully connected networks. Moreover the degree of each node in the initial network should be at least 1 in order to obtain entirely connected networks. New nodes are successively added to the network. Each new node is connected to t (limited by l) nodes already belonging to the network in respect with a probability proportional to their current degree.

Examples

n=50;//network size
l0=5;//a maximum of 5 links are created for any created node
L=1000;//network square area side 
[g,d]=NARVAL_T_BarabasiAlbert(n,l0,L);//application of NARVAL_T_BarabasiAlbert
ind=1;//window index
f=NARVAL_G_ShowNodesIndex(g,ind);//graph visualization

Dependency

NARVAL_F_XYRand, NARVAL_F_Random, NARVAL_F_RandWtRepl, NARVAL_G_MakeGraph, 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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