Dehne et al. present a BSP/CGM algorithm for computing a spanning tree and the connected components of a graph, that requires O(log p) communication rounds, where p is the number of processors. It requires the solution of the Euler tour problem which in turn is based on the solution of the list ranking problem. We present a new approach that does not need to solve the Euler tour or the list ranking problem. It is based on the integer sorting algorithm which can be implemented efficiently on the BSP/CGM model [1].