Large-scale comparative genomics studies offer valuable resources for understanding both functional and evolutionary rate constraints. It is suggested that constraint aligns with the topology of genomic protein-protein interaction (PPI) networks, increasing toward the center, with intermediate nodes combining relaxed constraint with higher contributions to the phenotype due to pleiotropy. However, this pattern has yet to be demonstrated in vertebrates. Here I show that constraint intensifies toward the network's center in both yeast and placental mammals. Genes with rate changes associated with emergence of mammalian hibernation cluster mostly toward intermediate positions, with higher constraint in faster-evolving genes, which is indicative of a “sweet spot” for adaptation. Network node metrics could therefore predict genomic regions favored for adaptation even in clades lacking empirical constraint data. To explore this idea, I used lacertid lizards as example for such group of species without empirical constraint data, and show that genes with signatures of selection in response to a latitudinal environmental gradient likewise cluster in more intermediate positions, which is even more pronounced in genes which have been re-used for this purpose independently multiple times across vertebrates. These particular genes further reveal a strong correlation between evolutionary rate and preference for cooler environments, affirming prior results that the diversification of lacertid lizards is predominantly driven by adaptation to cooler climates. In conclusion, genome architecture offers important clues about the co-evolution of protein-coding genes that respond to environmental stimuli, thereby enhancing our comprehension of the resilience and adaptability of organisms in the face of climate change.