Researchers have developed a new statistic to analyze shortest-path anisotropy in graph representations of black-hole geometries. This tool allows for the study of how geometric information is encoded in the shortest-path structure within curved spaces. The method is based on the cubic mean deviation of the logarithm of the number of shortest paths from a reference vertex to other vertices on a specific graph-distance shell.

The statistic was tested on graph discretizations of static, spherically symmetric black-hole embedding geometries, including Schwarzschild/Flamm, Reissner-Nordström, Bardeen, and Hayward backgrounds. It was observed that the statistic exhibits a stable radial organization strongly correlated with the logarithmic Kretschmann curvature profile. This pattern was not reproduced in matched-flat controls, highlighting the diagnostic's sensitivity to curvature.

For Reissner-Nordström geometries with $M=1/2$ and charges $Q=0,\ldots,0.4$, the seed-averaged radial and curvature-profile correlations remained stable across ten random seeds. Similar robustness was found for Bardeen and Hayward parameter scans. Additional tests on non-black-hole benchmark surfaces indicate that the statistic is not a universal pointwise curvature scalar; rather, it is a curvature-sensitive graph diagnostic whose interpretation depends on the graph construction and control geometry.

These results suggest that shortest-path multiplicity anisotropy can provide a useful probe of curvature-organized structure in graph discretizations of black-hole embedding geometries. This advance offers a new perspective for understanding the fundamental properties of spacetime near these compact objects, opening avenues for future research into the relationship between discrete geometry and continuous curvature.