The rheological properties of a hierarchically structured supramolecular soft material are mainly determined by the structure of its network. Controlling the thermodynamic driving force of physical gels (one type of such materials) during the formation has proven effective in manipulating the network structure due to the nature of nucleation and growth of the fiber network formation in such a supramolecular soft material. Nevertheless, it is shown in this study that such a property can be dramatically influenced when the volume of the system is reduced to below a threshold value. Unlike un-confined systems, the network structure of such a soft material formed under volume confinement contains a constant network size, independent of the experimental conditions, i.e. temperature and solute concentration. This implies that the size of the fiber networks in such a material is invariable and free from the influence of external factors, once the volume is reduced to a threshold. The observations of this work are significant in the control of the formation of fibrous networks in materials of this type.