Percolation transition of K-destinations reveals universal backbone of urban mobility networks

Cities are held together by a small subset of recurrent origin-destination ties, but extracting this backbone from noisy mobility data remains difficult, and most models still prioritize distance over connectivity. We build directed mobility networks from 48 months of mobile-phone data across eight US cities (2018-2021) and apply a rank-based percolation filter that retains, for each origin, its top- $K$ destinations. Defining $K^{\ast }$ as the smallest cutoff that yields a strongly connected network, we find that city-specific thresholds cluster tightly across space and time, with a representative value near $K\approx 130$ . Degree-preserving and gravity-style baselines do not recover this scale, underscoring the importance of selectively preserved long-range functional ties. We then define $\text{PPD}\left(K\right)$ , an origin-level mobility concentration measure, and show that socioeconomic associations peak around the percolation-derived integration regime. Together, these findings offer a principled method to extract a minimal mobility backbone and connect its structure to persistent socioeconomic variation.