Perform the assortativity coefficient of a graph.
[A]=NARVAL_G_Assortativity(JDD)
Joint Degree Distribution.
Assortativity Coefficient.
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.
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 | ![]() | ![]() |