Although 1D conductance histograms provide a convenient method to visualize singlemolecule conductance distributions, peak conductance values may not fully reflect junction characteristics, particularly when conductance depends on molecular extension. To understand how molecular conductance depends on junction separation, we constructed 2D molecular conductance histograms by plotting conductance as a function of tip displacement (Figs. ). Ladder molecules exhibit remarkably constant conductance values during junction displacement (Figs. , Supplementary Figs. ). To quantitatively understand the variation in molecular conductance as a function of tip displacement, we determined the slope of trend lines fit to the peak conductance value as a function of junction displacement using linear regression (Fig. ) (Methods). Our results show that the most probable conductance values of ladder molecules (L1-PF6-L4-PF6) exhibit extremely small changes in molecular conductance G/G0 as a function of electrode separation x (dlog(G/G0)/dx ≈ -0.1 nm -1 ), indicating the presence of robust and stable junctions with a nearly displacement-independent conductance. In contrast, non-ladder analogs (N1-PF6-N3-PF6) exhibit broadly distributed molecular conductance peaks spanning several orders of magnitude of conductance in the underlying ensemble (Figs. ). Non-ladder analogs (N1-PF6-N3-PF6) show much larger changes in molecular conductance as a function of junction displacement (dlog(G/G0)/dx ≈ -7 nm -1 ). These results clearly show more variability in the molecular conductance of non-ladder molecules compared to the ladder analogs. In addition to the high conductance peak, L1-PF6 and L2-PF6 also exhibited a less welldefined low conductance peak. To understand the origin of these conductance features, we used a 2D correlation analysis of single-molecule conductance trajectories (Fig. ) that showed a negative correlation between the two molecular conductance populations, indicating that either one or the other conductance feature occurs in individual singlemolecule traces. These results suggest that these two molecular conductance features arise due to different molecular junction conformations (static heterogeneity) rather than dynamic molecular junction conformations that interchange during the molecular pulling trajectory (dynamic heterogeneity). We further analyzed the molecular conductance features of the ladder-type molecules using flicker noise analysis . Flicker noise analysis provides a measure of conductance fluctuations that reveals information regarding molecular conduction pathways (e.g., through-bond or through-space conductance) . In this experiment, we performed holding-mode conductance measurements where molecular junctions were held at a fixed displacement for ~100 ms. Conductance traces surviving the holding period are then selected and their noise power was determined by integrating the conductance noise power spectral density (PSD) in a frequency range between 100 Hz to 1000 Hz (Methods), as previously reported . Prior work has shown that the conductance tends to have smaller variations for through-bond conduction pathways . On the other hand, fluctuations in conductance are typically larger for through-space conduction pathways, where chemical bonds do not cover the entire conduction pathway and electrons tunnel through space to complete the circuit. Prior work has shown that plotting normalized noise power (noise power/G n ) versus average normalized conductance G yields a power-law dependence where the scaling exponent n ≈ 1 indicates a through-bond conduction pathway whereas n ≈ 2 indicates a through-space conduction pathway .