  We study the compact localized scattering resonances of periodic and
aperiodic chains of dipolar nanoparticles by combining the powerful Equitable
Partition Theorem (EPT) of graph theory with the spectral dyadic Green's matrix
formalism for the engineering of embedded quasi-modes in non-Hermitian open
scattering systems in three spatial dimensions. We provide analytical and
numerical design of the spectral properties of compact localized states in
electromagnetically coupled chains and establish a connection with the
distinctive behavior of Bound States in the Continuum. Our results extend the
concept of compact localization to the scattering resonances of open systems
with arbitrary aperiodic order beyond tight-binding models, and are relevant
for the efficient design of novel photonic and plasmonic metamaterial
architectures for enhanced light-matter interaction.
