Technologically relevant magnetic nanoparticles for biomedicine are rarely noninteracting single-domain nanoparticles; instead, they are often interacting, with complex physical and magnetic structures. In this paper, we present both experimental and simulated magnetic hysteresis loops of a system of magnetic nanoparticles with significant interparticle interactions and a well-defined intraparticle structure which are used for magnetic nanoparticle hyperthermia cancer treatment. Experimental measurements were made at 11 K on suspensions of magnetic nanoparticles dispersed in H2O which have been frozen in a range of applied magnetic fields to tune the interparticle interactions. Micromagnetic simulations of hysteresis loops investigated the roles of particle orientation with respect to the field and of particle chaining in the shape of the hysteresis loops. In addition, we present an analysis of the magnetic anisotropy arising from the combination of magnetocrystalline and shape anisotropy, given the well-defined internal structure of the nanoparticles. We find that the shape of the experimental hysteresis loops can be explained by the internal magnetic structure, modified by the effects of interparticle interactions from chaining.