Agglomeration of nanoparticles occurs in a number of colloidal systems related, for example, to material processing and drug delivery. The present work is motivated by the need to improve fundamental understanding of the agglomeration and structure formation processes that occur in catalyst inks used for the fabrication of polymer electrolyte fuel cells (PEMFCs). Particle dynamics simulations are performed to investigate agglomeration under various conditions. The interaction between particles is defined using realistic physical potentials, rather than commonly used potential models, and a novel analysis of the agglomeration and structure formation process is performed using network science concepts. The simulated systems correspond to catalyst inks consisting primarily of carbon nanoparticles in solution. The effect of various conditions such as different force magnitude, shape of the force function, concentration etc. are investigated in terms of network science parameters such as average degree and shortest path. An "agglomeration timescale" and a "restructuring timescale" introduced to interpret the evolution of the agglomeration process suggest that the structure, which has a strong impact on the performance of the eventual catalyst layer, can be controlled by tuning the rate at which particles are added based on the restructuring timescale.