Random partition is the cornerstone of atlas-free brain network analysis which can be used for multiscale analysis and comparison of cohorts with different brain sizes. The random parcels should be uniform to avoid additional variability from different parcel areas. In this study a uniform random partition of meshed surface is proposed considering geodesic distances and parcel areas. The partition results showed that proposed method can partition surface into any given number of parcels with similar areas. With repeating network analysis using proposed uniform parcels, results showed low intra-subject variations of global network measures.