Abstract-Structural transformations in a model ferrofluid in the absence of an external magnetic field have been theoretically studied. The results agree with well known laboratory experiments and computer simula tions in showing that, if the concentration of particles and their magnetic interaction energy are below certain critical values, most particles form separate linear chains. If these parameters exceed the critical values, most particles concentrate so as to form branched network structures. The passage from chains to network has a continuous character rather than represents a discontinuous first order phase transition.