# Generating matrix as follows

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NeGM on 13 May 2021
Edited: NeGM on 25 May 2021
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!

David Hill on 13 May 2021
Graph has to be a polygon.
numNodes=6;
a=randperm(numNodes);
b=circshift(a,1);
g=graph(a,b);
plot(g);
NeGM on 13 May 2021
Hey David, Thank you it works pretty well!

Matt J on 13 May 2021
Edited: Matt J on 13 May 2021
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 on 13 May 2021
Thank you