clear all
N=20;
P=0.2; %Probability of an edge being present at a node
C=1000;

for count=1:C
    E=(rand(N,N)<P);
    for ij=1:N
        E(ij,ij)=0;
    end
    e=sparse(E);
    Node1=ceil(N*rand);
    Node2=ceil(N*rand);
    while Node2==Node1
        Node2=ceil(N*rand);
    end
    [d(count)]=graphshortestpath(e,ceil(N*rand),ceil(N*rand));
end

view(biograph(e,[1:N],'EdgeType','straight'))

InfiniteDist=sum(d==Inf);
d(d==Inf)=0;
d=sparse(d);
num=1;
h=[];

while sum(h)<(C-InfiniteDist)
    h(num)=sum(d==num);
    num=num+1;
end

for node=1:N
TotalDeg(node)=sum(E(node,:))+sum(E(:,node));
end

figure
hist(TotalDeg,[1:num])
title('Single Realization of the Distribution of Total Degree at Each Node')
xlabel('Degree')
ylabel('Number of Nodes with Degree')
figure
y1=h/C;
bar(1:num,y1);
title('Asymptotic Shortest Path between Two Random Nodes')
xlabel('Path Length')
ylabel({'Percentage of Random Graphs with N Nodes';'and Edge Probability of P'})
hold on
y2=normpdf([1:0.01:num+1],mean(d),std(d));
plot(1:0.01:num+1,y2,'r')
hold off