%%% Random Graphs
clc
format compact
format short g
% Fixes the Random Number System
% Comment out the next line to change the output
rand('state',357) 
%% A small graph
n=10; % # of Vertices
p=0.45; % Probability of Connection

A=rand(n);
A=(A+A')/2;
p1=sqrt(p/2);
B = (A<p1);
Killer = ones(n)-eye(n);
B1 = Killer.*B
C=zeros(n);
C=(B-B^n)/(eye(n)-B);
C1=(C>0);
[1:n;sum(B);sum(C1)]'
W=10*rand(n)+0.5;
Weights=round((W+W')/2);
D = Weights.*B1


%% A larger random graph
n=100; % # of Vertices
p=0.04; % Probability of Connection

A=rand(n);
A=(A+A')/2;
p1=sqrt(p/2);
B = (A<p1);
Killer = ones(n)-eye(n);
B2 = Killer.*B;
C = (B-B^(n+1))/(eye(n)-B);
C2=(C>0);
[1:n;sum(B);sum(C2)]'