We introduce three representation-specific descriptors of one-particle \(\varvec{\pi }\) -electron coherence. A spin-summed 1-RDM is transformed to the symmetric Löwdin representation and projected onto a specified atom-resolved \(\varvec{\pi }\) subspace. Frobenius norms of the resulting interatomic blocks define a weighted molecular graph whose normalized accumulated weight \(\varvec{I}\) , graph-distance range \(\varvec{\xi }\) , and leading-axis ratio \(\varvec{A_{\pi }}\) quantify coherence strength, topological extent, and directional organization. Controlled tests show that qualitative trends are stable across HF, B3LYP, \(\varvec{\omega }\) B97X, and unrelaxed MP2 1-RDM protocols, whereas the absolute value of \(\varvec{I}\) is more sensitive than \(\varvec{\xi or A_{\pi }}\) to the basis and the representation/projection protocol. Twisting butadiene reduces \(\varvec{I}\) to one third of its planar value and suppresses the terminal graph-distance contribution by more than 90%, while short-range fragment coherence remains. Across polyenes, acenes, isomeric benzenoids, heteroaromatics, cyclic aromatic and antiaromatic systems, and helicenes, the three quantities resolve distinct responses to chain extension, annelation topology, heteroatom participation, electron count, bond alternation, and nonplanar embedding.
