How to reset pointers between nodes in a singly linked list to swap elements?

Question

C++ / C#

It is necessary to swap elements for selection sorting. There is the following function

void Sort()
{
    node *h = HEAD, *i, *j, *next_i;
    for(i = h; i!=NULL && i->NEXT!=NULL; i=i->NEXT)
    {
        node *min;
        min = i;
        for(j = i->NEXT; j!=NULL ; j=j->NEXT)
        {
            if(j->DATA < min->DATA)
                min=j;
        }
        if(min!=i)
        {
            int temp;
            temp = min->DATA;
            min->DATA = i->DATA;
            i->DATA = temp;
        }
    }
    HEAD = h;
}

The function works, but instead of the pointers, the values ​​stored in the nodes change. As far as I understand, this is contrary to the principles of working with lists, because there, the main idea is to swap pointers, not the value of the list node itself.
Actually a question how to make it in this case?