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NARVAL >> NL_G: Graph > NL_G_Assortativity

NL_G_Assortativity

Perform the assortativity coefficient of a graph.

Calling Sequence

[A] = NL_G_Assortativity(J)

Arguments

J :

Joint degree distribution.

A :

Assortativity coefficient.

Description

NL_G_Assortativity performs the assortativity coefficient A of the graph G defined by its joint degree distribution J. A provides information about how vertices of different types (degree) are preferentially connected amongst themselves. It is defined by where and with and . 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;//maximum number of new links per node
L=1000;//network square area side 
[g,dd]=NL_T_BarabasiAlbert(n,l0,L);//generation of the topology
ind=1;//window index
[f]=NL_G_ShowGraph(g,ind);//graph visualization
[d,dv]=NL_G_GraphDegreeDist(g);//extraction of the node degree distribution
m=max(dv);//maximum degree
w=2;//window index
JDD=NL_G_JointDegreeDist(g.name,g.head,g.tail,dv,m,w);//performance of JDD
[A]=NL_G_Assortativity(JDD)//application of NL_G_Assortativity

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