We study numerically the interaction between particles in a nematic liquid crystal mediated by its elastic distortions with the aid of the Landau-de Gennes continuum theory. We consider the cases where two particles impose rigid normal anchoring on their surfaces and are accompanied by a hyperbolic hedgehog defect. As a function of the distance between the centers of the particles D, we evaluate the force f acting on the particles by integrating the stress tensor. The result is well described by a power law f proportional to D-x. When the "dipoles", composed of a particle and a hyperbolic hedgehog, are in parallel directions, the interaction is attractive and the exponent is x similar or equal to 4, consistent with the experimental observations together with the theoretical expectation of the dipole-dipole interaction. For antiparallel dipoles, repulsive interaction is observed and x similar or equal to 3.6, slightly stronger than the dipole-dipole interaction.