Perform the assortativity coefficient of a graph.
[A] = NL_G_Assortativity(J)
Joint degree distribution.
Assortativity coefficient.
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).
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 | ![]() | ![]() |