Self-assembled clusters of metallic nanoparticles separated by nanometric gaps generate strong plasmonic modes that support both intense and localized near fields. These find use in many ultrasensitive chemical and biological sensing applications through surface enhanced Raman scattering (SERS). The inability to control at the nanoscale the structure of the clusters on which the optical response crucially depends, has led to the development of general descriptions to model the various morphologies fabricated. Here, we use rigorous electrodynamic calculations to study clusters formed by a hundred nanospheres that are separated by similar to 1 nm distance, set by the dimensions of the macrocyclic molecular linker employed experimentally. Three-dimensional (3D) cluster structures of moderate compactness are of special interest since they resemble self-assembled clusters grown under typical diffusion-limited aggregation conditions. We find very good agreement between the simulated and measured far-field extinction spectra, supporting the equivalence of the assumed and experimental morphologies. From these results we argue that the main features of the optical response of two- and three-dimensional clusters can be understood in terms of the excitation of simple units composed of different length resonant chains. Notably, we observe a qualitative difference between short- and long-chain modes in both spectral response and spatial distribution: dimer and short-chain modes are observed in the periphery of the cluster at higher energies, whereas inside the structure longer chain excitation occurs at lower energies. We study in detail different configurations of isolated one-dimensional chains as prototypical building blocks for large clusters, showing that the optical response of the chains is robust to disorder. This study provides an intuitive understanding of the behavior of very complex aggregates and may be generalized to other types of aggregates and systems formed by large numbers of strongly interacting particles.