Background Changes in epithelial cell shape reflects optimal cell packing and the minimization of surface free energy, but also cell–cell interactions, cell proliferation, and cytoskeletal rearrangements. Results Here, we studied the structure of the rat pleura in the first 15 days after birth. After pleural isolation and image segmentation, the analysis demonstrated a progression of epithelial order from postnatal day 1 (P1) to P15. The cells with the largest surface area and greatest shape variability were observed at P1. In contrast, the cells with the smallest surface area and most shape consistency were observed at P15. A comparison of polygonal cell geometries demonstrated progressive optimization with an increase in the number of hexagons (six‐sided) as well as five‐sided and seven‐sided polygons. Analysis of the epithelial organization with Voronoi tessellations and graphlet motif frequencies demonstrated a developmental path strikingly distinct from mathematical and natural reference paths. Graph Theory analysis of cell connectivity demonstrated a progressive decrease in network heterogeneity and clustering coefficient from P1 to P15. Conclusions We conclude that the rat pleura undergoes a striking change in pleural structure from P1 to P15. Further, a geometric and network‐based approach can provide a quantitative characterization of these developmental changes. Key Findings Evolving topological order of the pleura within the first two weeks after birth: decrease in shape variability increase in 6‐sided polygons decrease in network heterogeneity