" I would prefer the matrix to be symmetric." Why should it be? If person 1 and 2 are associated with group 4, it does not mean that person 4 is associated with group 1 and 2. There's not even a guarantee your matrix will be square unless you have the same number of groups as persons.
"Don't send me the link to matlab sparse page, please. I don't get it." Maybe you should try getting it, otherwise you won't get very far.
demodata = [1 5
1 3
2 4
1 4
2 1
3 2];
connections = sparse(demodata(:, 1), demodata(:, 2), 1)
Also note that your original storage is actually more efficient in term of memory than the sparse matrix since you don't have to store the '1' that carries no information.
