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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 defined by its joint degree distribution JDD. It tells how vertices of different types (degree) are preferentially connected amongst themselves. It is defined by r=(r1-r2)/(1-r2) where r1={sum i=1 to kmax} JDD(i,i) and r2={sum i=1 to kmax}ai*bi with ai={sum j=1 to kmax}JDD(i,j) and bj={sum i=1 to kmax}JDD(i,j). kmax is the maximum node degree in the graph. A belongs to [-1:1]. Disassortative graphs with negative A have an excess 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.

Examples

n=300;//network size
l0=5;//a maximum of 5 links are created for any created node
L=1000;//network square area side 
[g,dd]=NARVAL_T_BarabasiAlbert(n,l0,L);//generation of the topology
ind=1;
[f]=NARVAL_G_ShowGraph(g,ind);
[d,dv]=NARVAL_G_GraphDegDistWD(g);//extraction of the node degree distribution
m=max(dv);
w=2;
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

Author

http://wwwen.uni.lu/interdisciplinary_centre_for_security_reliability_and_trust

Contact

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