Detecting symmetry in sparse matrix

So I need to detect symmetry between 2 arrays of linked lists. One array represents rows in a sparse matrix (a table where empty values do not exist and thus do not waste space) and the other represents columns. I need to detect to see if the matrix is symmetrical, and I don't know how to navigate through the matrix properly to test this. If someone could please describe the proper loops and checks to make it would be great. Thanks!