Genome architecture has emerged as a critical element of transcriptional regulation, although its role in the control of cell identity is not well understood. Here we use transcription factor (TF)-mediated reprogramming to examine the interplay between genome architecture and transcriptional programs that transition cells into the myogenic identity. We recently developed new methods for evaluating the topological features of genome architecture based on network centrality. Through integrated analysis of these features of genome architecture and transcriptome dynamics during myogenic reprogramming of human fibroblasts we find that significant architectural reorganization precedes activation of a myogenic transcriptional program. This interplay sets the stage for a critical transition observed at several genomic scales reflecting definitive adoption of the myogenic phenotype. Subsequently, TFs within the myogenic transcriptional program participate in entrainment of biological rhythms. These findings reveal a role for topological features of genome architecture in the initiation of transcriptional programs during TF-mediated human cellular reprogramming.