Generating matrix as follows

Hi Everyone,

I'd like to create random adjacency matrices for networks in the following form (see image), as you can see I have 6 nodes (n = 6) and each node must have 2 connections (degree = 2) to two other nodes chosen randomly. So the sum of each row must equal 2(or whatever value "degree" is assigned). The matrix must be symmetric with zeros along the diagonal (properties of the adjacency matrix). I have written a code that generates random adjacency matrices but Imnot sure how to constraint the program such that each node has exaclty 2 random connections.

A = zeros(n,n);  % Create initial matrix 
for i = 1:n
    for j = 1:n 
        if i==j
            A(i,j)=0;             % Zero values in the diagonal entries                 
        else
            A(i,j)=round(rand);   % Choosing random 0 and 1 values
            A(j,i)=A(i,j);        % Make A matrix symmetric        
        end
    end
end                                             

Any help is greatly appreciated, Thank you!

Answer 1

[David Hill]

Graph has to be a polygon.

numNodes=6;
a=randperm(numNodes);
b=circshift(a,1);
g=graph(a,b);
plot(g);
m=full(adjacency(g));

[NeGM]

Hi David,

this is perfect given that each node has 2 connections but I'd like to know how to contraint it si that I can change the number of nodes and edges for instance how can I generate an adjacency matrix with n = 20 and degrees = 3 (number of connections) to 3 different nodes. any suggestions? Thank you so much in advance

[David Hill]

Some combinations of nodes and degrees will not work.

while 1
numNodes=20;
degrees=3;
n=repelem(1:numNodes,degrees);
s=[];t=[];
flag=1;
while ~isempty(n)
    N=unique(n);
    a=sum(n==N(1));
    b=nchoosek(N(2:end),a);
    try 
        c=b(randi(length(b)),:);
    catch 
        flag=0;
        break;
    end
    s=[s,n(n==N(1))];
    t=[t,c];
    n=n(a+1:end);
    for k=1:a
        try
            n(find(n==c(k),1))=[];
        catch 
            flag=0;
            break;
        end
    end
end
if flag
    g=graph(s,t);
    plot(g);
    m=full(adjacency(g));
    break;
end
end

[NeGM]

Hey David, Thank you it works pretty well!

Answer 2

[Matt J]

Perhaps as follows,

n=6;

T=nan(n,2);

map=isnan(T);

while any(map(:))
   
    [i,~]=find(map,1);
    
    if ~map(i,1)
       exclude=[i,T(i,1)]; 
    elseif  ~map(i,2)
        exclude=[i,T(i,2)];
    else
        exclude=i;
    end
    
    pool=setdiff(find(any(map,2)),exclude);
    
    if isempty(pool)
       T=nan(n,2); map=isnan(T); continue 
    end
    
    p=numel(pool);
    
    j=pool(randi(p));
    
    if  map(i,1), 
        T(i,1)=j; 
        map(i,1)=0;
    else, 
        T(i,2)=j; 
        map(i,2)=0;
    end
    
    if  map(j,1), 
        T(j,1)=i; 
        map(j,1)=0;
    else, 
        T(j,2)=i; 
        map(j,2)=0;
    end
    
end
s=[(1:n), (1:n)].';
t=[T(:,1); T(:,2)];

st=unique(sort([s,t],2),'rows');

G=graph(st(:,1),st(:,2));

degree(G)

ans = 6×1

2 2 2 2 2 2

[NeGM]

hi Matt,

Under your code each node has a degree of 4, is there a way to contraint the connection to only have a specified number? Thank you

[Matt J]

Fixed it.

[NeGM]

Thank you