In this paper, the authors study the structure of the Load-based Spanning Tree (LST) that carries the maximum weight of the Erdos-Renyi (ER) random network. The weight of an edge is given by the edge-betweenness centrality, the effective number of shortest paths through the edge. They find that the LSTs present very inhomogeneous structures in contrast to the homogeneous structures of the original networks. Moreover, it turns out that the structure of the LST changes dramatically as the edge density of an ER network increases, from scale free with a cutoff, scale free, to a starlike topology.