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NARVAL >> NARVAL > NARVAL_G_Betweenness

NARVAL_G_Betweenness

Perform the betweenness of a node inside a graph.

Calling Sequence

[B,S] = NARVAL_G_Betweenness(ERT,l)

Parameters

ERT :

enhanced routing table.

l :

node index.

B :

betweeness.

S :

betweeness coefficients.

Description

NARVAL_G_Betweenness performs the betweeness B of the node l inside the graph g represented by its enhanced routing table ERT. ERT stores all paths between any couple of distinct nodes within the network. ERT can be generated with the application of NARVAL_R_ERoutingTable on routing tables created from NARVAL_R_TFlood, NARVAL_R_TDijkstra, or NARVAL_R_TBellmanFord. For a better convenience, we already generated a scenario whith the creation of a graph composed by 100 nodes. We have also performed 5 enhanced routing tables [rt1,rt2,rt3,rt4,rt5] providing multiple paths for each connection between two nodes. The route between the nodes i and j can be read at the line of index (i-1)*n+j where n represents the network size. Then for each path stored into a single line, its hop length can be found in the first column, followed by its length and finally the path composed by a list of nodes ([hop length | length | path]). Let Sij be the number of shortest paths between the nodes i and j. Let Sijl be the number of shortest paths between the nodes i and j going through the node l. Its betweenness is B={Σ i j}{Sijl/Sij}. B is normalized by n(n-1) where n is the graph size (WIKIPEDIA).

Examples

[path]=NARVAL_F_NARVALPath();//path to NARVAL module
path=path+'/demos/';//folder path
load(path+'RoutingTables_topo_100.dat','pt','rt1','rt2','rt3','rt4','rt5');//loading of the network routing tables
l=79;//node index
[B,S]=NARVAL_G_Betweenness(rt1,l);//application of NARVAL_G_Betweenness 
B
S

Dependency

NARVAL_R_NodeInPaths

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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