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NARVAL >> NARVAL > NARVAL_G_LocalClustering

NARVAL_G_LocalClustering

Perform the local clustering of the k-degree nodes of a graph.

Calling Sequence

[ik,LN,LC] = NARVAL_G_LocalClustering(g,k)

Parameters

g :

graph.

k :

node degree.

ik :

index of k-degree nodes.

LN :

vector with the number of links between neighbors of the k-degree nodes.

LC :

local clustering.

Description

NARVAL_G_LocalClustering performs the local clustering LC of the k-degree nodes within the graph g. If mnn(k) is the average number of links between the neighbors of k-degree nodes, the local clustering LC is the ratio of this number to the maximum possible such links: LC(k)=2*mnn(k)/(k*(k-1)). If two neighbors of a node are connected, then these three nodes form together a triangle (3-cycle). Thus the local clustering corresponds to the average number of 3-cycles involving k-degree nodes (WIKIPEDIA).

Examples

n=300;//network size
l0=5;//a maximum of 5 links are created for each new node
L=1000;//network square area side 
[g,dd]=NARVAL_T_BarabasiAlbert(n,l0,L);//generation of the topology
ind=1;//window index
[f]=NARVAL_G_ShowGraph(g,ind);//graph visualization
[d,dv]=NARVAL_G_GraphDegDistWD(g);//extraction of the node degree distribution
m=max(dv);//maximum degree
LCv=[];
for i=2:m
[ik,LN,LC]=NARVAL_G_LocalClustering(g,i);//application of NARVAL_G_LocalClustering
LCv=[LCv LC];
end
LCv

Dependency

NARVAL_G_GraphDegDistWD, NARVAL_G_NodeNeighbors, NARVAL_G_InternLinks

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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