Although multiple hydrophobic, aromatic π-π, and electrostatic interactions are proposed to be involved in amyloid fibril formation, the precise interactions within amyloid structures remain poorly understood. Here, we carried out detailed quantum theory of atoms-in-molecules (QTAIM) analysis to examine the hydrophobic core of amyloid parallel and antiparallel β-sheet structures, and found the presence of multiple inter-strand and intra-strand topological neighborhoods, represented by networks of through-space bond paths. Similar bond paths from side chain to side chain and from side chain to main chain were found in a single β-strand and in di- and tripeptides. Some of these bond-path networks were enhanced upon β-sheet formation. Overall, our results indicate that the cumulative network of weak interactions, including various types of hydrogen bonding (X-H-Y; X, Y = H, C, O, N, S), as well as non-H-non-H bond paths, is characteristic of amyloid β-sheet structure. The present study postulated that the presence of multiple through-space bond-paths, which are local and directional, can coincide with the attractive proximity effect in forming peptide assemblies. This is consistent with a new view of the van der Waals (vdW) interactions, one of the origins of hydrophobic interaction, which is updating to be a directional intermolecular force.