Given a connected, undirected and m-partite complete graph G=(V1∪V2∪...∪Vm;E), the Generalized Minimum Spanning Tree Problem (GMSTP) consists in finding a tree with exactly m−1 edges, connecting the m clusters V1,V2,...,Vm through the selection of a unique vertex in each cluster. GMSTP finds applications in network design, irrigation agriculture, smart cities, data science, among others. This paper presents a new multigraph mathematical formulation for GMSTP which is compared to existing formulations from the literature. The proposed model proves optimality for well-known GMSTP instances. In addition, this work opens new directions for future research to the development of sophisticated cutting plane and decomposition algorithms for related problems.