A novel method for investigating the multicenter bonding patterns in molecular systems by means of the so-called Electron Density of Delocalized Bonds (EDDB) is introduced and discussed. The EDDB method combines the concept of Jug's bond-order orbitals and the indirect ("through-bridge") interaction formalism and opens up new opportunities for studying the interplay between different atomic interactions as well as their impact on both local and global resonance stabilization in systems of conjugated bonds. Using several illustrative examples we demonstrate that the EDDB approach allows for a reliable quantitative description of diverse multicenter delocalization phenomena (with special regard to evaluation of the aromatic stabilization in molecular systems) within the framework of a consistent theoretical paradigm.