Generating matrix as follows
显示 更早的评论
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!
采纳的回答
David Hill
2021-5-13
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));
3 个评论
NeGM
2021-5-13
David Hill
2021-5-13
编辑：David Hill
2021-5-13
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
2021-5-13
更多回答（1 个）
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)
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