The availability of unprecedented datasets detailing the organization of chromatin across species, developmental stages, cell types and diseases invites an integrated analysis of genome organization in three dimensions and its biological significance.In this study we attempt to formalize a hypothesis according to which the topological properties of the chromatin network can impact phenotypes, such as plasticity and variability. Our observations lead us to reconsider the theory according to which cancer cells re-acquire pluripotency through a reactivation of early evolutionary programs characteristic of species lacking complex body plans or even multicellularity.Recent work investigating gene variability across tissues and individuals in multiple species has shown that promoter sequence characteristics can be predictive of gene expression variability. Exploiting this dataset and others, we show that genes with specific promoter features and associated similar values of expression variability tend to have specific epigenomic marks and form preferential interactions in 3D, as quantified by chromatin assortativity. We then investigate whether rearrangements of the 3D topology of the chromatin network in differentiation and oncogenesis can change these associations between gene regulation and evolutionary age. We observed that evolutionary older genes, also broadly corresponding to the least variable genes, are strongly clustered in the chromatin network.We characterize the topology of promoter-centered chromatin networks as well as assortativities of gene ages and expression variability in multiple datasets capturing topological changes in differentiation (embryonic stem cells, B cells) and find some of these changes to be reversed during oncogenesis.