The recently predicted induced magnetic monopole and the topologically-quantized magnetoelectric effect are fundamental attributes of topological states of matter. Using an ultrasensitive nanoSQUID, acting as a tunable scanning electric charge, we induce and directly image the topological microscopic currents generating the magnetic monopole in a graphene quantum Hall electron system. We find a rich and complex behavior governed by counterpropagating topological and nontopological equilibrium-state currents that is not captured by the monopole models. We also directly image the quantum Hall edge states revealing that the downstream topological edge currents in the incompressible regions are counterbalanced by heretofore unobserved nontopological upstream currents flowing in the adjacent compressible strips. The intricate patterns of the equilibrium-state orbital currents, imaged for the first time, provide new insights into the microscopic origins of the topological and nontopological charge and energy transport in quantum Hall systems.