<p>Classical variogram analysis groups squared increments by Euclidean separation. This choice is natural in homogeneous or approximately isotropic domains, but it can be misleading in heterogeneous permeability fields where physical coupling is controlled by pathways, barriers, facies continuity, or other forms of connectivity. This paper presents a reproducible workflow for variography in alternative metric geometries. We compare three lag definitions on a compact two-dimensional <i>x</i>–<i>z</i> slice of the SPE10 benchmark: Euclidean distance, graph-geodesic distance on a permeability-weighted grid graph, and diffusion distance obtained from the heat kernel of the normalized graph Laplacian. The graph-geodesic distance represents least-cost connectivity, whereas diffusion distance aggregates multi-path connectivity at a scale controlled by diffusion time <i>t</i>. We emphasize that the benchmark is a diagnostic and proxy-informed experiment: the graph is built from the available permeability/connectivity field, so the results should not be interpreted as blind prediction when no auxiliary connectivity information is available. Under this interpretation, diffusion distance provides a more coherent geometry for ordinary kriging than Euclidean or shortest-path distance in the examined highly heterogeneous field. We also show how heat-smoothed differences provide diffusion-wavelet-like detail bands whose variograms summarize scale-localized connectivity structure. The workflow connects geostatistical characterization with graph signal processing and is intended for settings where a prior geological model, facies model, hydraulic-property proxy, or simulation grid can provide connectivity information.</p>