clear all

N=5;  % Number of nodes
k=2;  % Number of edges per node in initial regular graph


% Calculate Regular Graph Measures

M=zeros(N,N);

for m=1:(k/2)
    M=M+diag(ones(N-m,1),m)+diag(ones(m,1),(N-m));
end
d=zeros(N,N);
for n=1:N
    for r=1:N
        d(n,r)=graphshortestpath(sparse(M),n,r);
    end
end
d(d==Inf)=NaN;
for q=1:N
    geodesics(q)=max(d(q,:));
end

LRegular=mean(geodesics);


% Calculate Random Graph Measures
for p=1:45
    G=M;
    for u=1:20
        for s=1:N-1
            for t=s+1:N
                if G(s,t)>0
                    a=unifSample([0 1],[(1-(0.02*p)) (0.02*p)]);
                    G(s,t)=G(s,t)-a;
                    if a==1
                        c=ceil((N-s)*rand);
                        G(s,s+c)=G(s,s+c)+1;
                    end
                end
            end
        end
        d=zeros(N,N);
        for n=1:N
            for r=1:N
                d(n,r)=graphshortestpath(sparse(G),n,r);
            end
        end
        d(d==Inf)=NaN;
        for q=1:N
            geodesicsR(q)=max(d(q,:));
        end
        MeanOfGeodesicsR(u)=mean(geodesicsR);
    end
    
    LRandom(p)=mean(MeanOfGeodesicsR);
    Ratio(p)=LRandom(p)/LRegular;
    
end

plot(0.01.*[1:2:90],Ratio,'r.')
axis([0 1 0 4])

hold on




% Calculate Random Graph Measures
for p=1:45
    G=M;
    for u=1:100
        for s=1:N-1
            for t=s+1:N
                if G(s,t)>0
                    a=unifSample([0 1],[(1-(0.02*p)) (0.02*p)]);
                    G(s,t)=G(s,t)-a;
                    if a==1
                        c=ceil((N-s)*rand);
                        G(s,s+c)=G(s,s+c)+1;
                    end
                end
            end
        end
        d=zeros(N,N);
        for n=1:N
            for r=1:N
                d(n,r)=graphshortestpath(sparse(G),n,r);
            end
        end
        d(d==Inf)=NaN;
        for q=1:N
            geodesicsR(q)=max(d(q,:));
        end
        MeanOfGeodesicsR(u)=mean(geodesicsR);
    end
    
    LRandom(p)=mean(MeanOfGeodesicsR);
    Ratio(p)=LRandom(p)/LRegular;
    
end

plot(0.01.*[1:2:90],Ratio,'r')
axis([0 1 0 4])
hold on


clear all


N=9;  % Number of nodes
k=6;  % Number of edges per node in initial regular graph


% Calculate Regular Graph Measures

M=zeros(N,N);

for m=1:(k/2)
    M=M+diag(ones(N-m,1),m)+diag(ones(m,1),(N-m));
end
d=zeros(N,N);
for n=1:N
    for r=1:N
        d(n,r)=graphshortestpath(sparse(M),n,r);
    end
end
d(d==Inf)=NaN;
for q=1:N
    geodesics(q)=max(d(q,:));
end

LRegular=mean(geodesics);


% Calculate Random Graph Measures
for p=1:45
    G=M;
    for u=1:20
        for s=1:N-1
            for t=s+1:N
                if G(s,t)>0
                    a=unifSample([0 1],[(1-(0.02*p)) (0.02*p)]);
                    G(s,t)=G(s,t)-a;
                    if a==1
                        c=ceil((N-s)*rand);
                        G(s,s+c)=G(s,s+c)+1;
                    end
                end
            end
        end
        d=zeros(N,N);
        for n=1:N
            for r=1:N
                d(n,r)=graphshortestpath(sparse(G),n,r);
            end
        end
        d(d==Inf)=NaN;
        for q=1:N
            geodesicsR(q)=max(d(q,:));
        end
        MeanOfGeodesicsR(u)=mean(geodesicsR);
    end
    
    LRandom(p)=mean(MeanOfGeodesicsR);
    Ratio(p)=LRandom(p)/LRegular;
    
end

plot(0.01.*[1:2:90],Ratio,'b.')
axis([0 1 0 4])

hold on




% Calculate Random Graph Measures
for p=1:45
    G=M;
    for u=1:100
        for s=1:N-1
            for t=s+1:N
                if G(s,t)>0
                    a=unifSample([0 1],[(1-(0.02*p)) (0.02*p)]);
                    G(s,t)=G(s,t)-a;
                    if a==1
                        c=ceil((N-s)*rand);
                        G(s,s+c)=G(s,s+c)+1;
                    end
                end
            end
        end
        d=zeros(N,N);
        for n=1:N
            for r=1:N
                d(n,r)=graphshortestpath(sparse(G),n,r);
            end
        end
        d(d==Inf)=NaN;
        for q=1:N
            geodesicsR(q)=max(d(q,:));
        end
        MeanOfGeodesicsR(u)=mean(geodesicsR);
    end
    
    LRandom(p)=mean(MeanOfGeodesicsR);
    Ratio(p)=LRandom(p)/LRegular;
    
end

plot(0.01.*[1:2:90],Ratio,'b')
axis([0 1 0 4])







%view(biograph(M,[1:N],'ShowArrows','off','EdgeType','straight','LayoutType','equilibrium'))
%view(biograph(G,[1:N],'ShowArrows','off','EdgeType','straight','LayoutType','equilibrium'))



%view(biograph(M,[1:N],'ShowArrows','off','EdgeType','straight','LayoutType','equilibrium'))
%view(biograph(G,[1:N],'ShowArrows','off','EdgeType','straight','LayoutType','equilibrium'))