Perform the betweenness of a node inside a graph.
[B,S] = NL_G_Betweenness(R,L)
Enhanced routing table.
Node index.
Betweeness.
Betweeness coefficients.
NL_G_Betweenness performs the betweeness B of the node I inside the graph G represented by its enhanced routing table R. R stores all paths between each couple of distinct nodes within the graph. R can be generated with the application of NL_R_RT2ERT on the routing tables created from NL_R_FloodRT, NL_R_DijkstraRT, or NL_R_BellmanFordRT. For a better convenience, we already generated a scenario whith the creation of a graph composed by 100 nodes. We have also performed 5 enhanced routing tables providing multiple paths for each connection between two nodes. The route between the nodes
and
can be extracted at the line of index
where
represents the graph size. Then for each path stored into a single line, its hop length can be found in the first column, followed by its length and finally the path composed by a list of nodes ([hop length | length | path]). Let
be the number of shortest paths between the nodes
and
. Let
be the number of shortest paths between the nodes
and
going through the node
. Its betweenness is
. B is normalized by
where n is the graph size (WIKIPEDIA).
[path]=NL_F_NLPath();//path to NARVAL module path=path+'/demos/';//folder path load(path+'RoutingTables_topo_100.dat','pt','rt1','rt2','rt3','rt4','rt5');//loading of the network routing tables l=79;//node index [B,S]=NL_G_Betweenness(rt1,l)//application of NL_G_Betweenness | ![]() | ![]() |