The jamming transition of an isotropically compressed granular packing is studied by means of molecular dynamics simulations. The system is shown to undergo a critical transition which is analyzed by looking at the topological structure of the force network. At the critical packing fraction there is a sudden growth of the number of polygons in the network. Above the critical packing fraction the number of triangles keeps growing while the number of the rest of polygons is weakly reduced. Then, we prove that in the jammed regime, there is a linear relationship between the number of triangles and the coordination number. Furthermore, the presence of these minimal structures is revealed to be connected with the evolution of some important topological properties, suggesting its importance to understand the physical properties of the packing and the onset of rigidity during the compression.