When we computing various network measures from a big graph $($connected$),$ we come across a term Beta $().$

a$)$ While calculating the network measures, explain why we need this and what is it's effect on the network measure of that graph?

b$)$ Now let assume that, for a fixed Beta $(),$ we have calculated the centrality measures, for all the nodes of the graph, and one node, say $x,$ has bigger value than other node, say $Y.$ Can we make the situation reverse $($for X & Y$),$ with different Beta $()$ value?

$[4$ Marks$]$