The absorption line shapes of a series of linear and star-shaped perylene diimide (PDI) complexes are evaluated theoretically and compared to experiment. The cyclic trimer and tetrahedral complexes are part of the symmetric series, characterized by a single interchromophoric coupling, J(0), between any two PDI chromophores. The measured spectra of all complexes show pronounced vibronic progressions based on the symmetric ring stretching mode at ~1400 cm(-1). The spectral line shapes are accurately reproduced using a Holstein Hamiltonian parametrized with electronic couplings calculated using time-dependent density functional transition charge densities. Although the "head-to-tail" linear complexes display classic J-aggregate behavior, the star-shaped complexes display a unique photophysical response, which is neither J- nor H-like. In the symmetric N-mers (N = 2-4), absorption and emission are polarized along N - 1 directions in contrast to linear complexes where absorption and emission remain polarized along the long molecular axis. In the symmetric complexes the red-shift of the 0-0 peak with increasing |J(0)|, as well as the initial linear rise of the 0-0/1-0 oscillator strength ratio with increasing |J(0)|, are independent of the number of PDI chromophores, N, and are markedly smaller than what is found in the linear series, where the shifts and ratios depend on N. Moreover, whereas the radiative decay rate, γ(r), scales with N and is therefore superradiant in linear complexes, γ(r) scales with N/(N - 1) in the symmetric complexes. Vibronic/vibrational pair states (two-particle states) are found to profoundly affect the absorption line shapes of both linear and symmetric complexes for sufficiently large coupling.