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NARVAL >> NARVAL > NARVAL_G_Assortativity

NARVAL_G_Assortativity

Perform the assortativity coefficient of a graph.

Calling Sequence

[A] = NARVAL_G_Assortativity(JDD)

Parameters

JDD :

Joint Degree Distribution.

A :

Assortativity Coefficient.

Description

NARVAL_G_Assortativity performs the assortativity coefficient A of the graph g defined by its joint degree distribution JDD. A provides information about how vertices of different types (degree) are preferentially connected amongst themselves. It is defined by r=(r1-r2)/(1-r2) where r1={Σ i=1..kmax} JDD(i,i) and r2={Σ i=1..kmax} ai*bi with ai={Σ j=1..kmax} JDD(i,j) and bj={Σ i=1..kmax} JDD(i,j). kmax is the maximum node degree within the graph. A belongs to [-1:1]. Disassortative graphs with negative A have an excess of radial edges connecting nodes of dissimilar degrees. Such networks are vulnerable to random failures and targeted attacks. Graphs with positive A are assortative and have an excess of edges connecting nodes of similar degrees (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
w=2;//window index
JDD=NARVAL_G_JDD(g.name,g.head,g.tail,dv,m,w);//performance of JDD
[A]=NARVAL_G_Assortativity(JDD);//application of NARVAL_G_Assortativity
A

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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