Broad domain promoters and super enhancers are regulatory elements that govern cell-specific functions and harbor disease-associated sequence variants. These elements are characterized by distinct epigenomic profiles, such as expanded deposition of histone marks H3K27ac for super enhancers and H3K4me3 for broad domains, however little is known about how they interact with each other and the rest of the genome in three-dimensional chromatin space. Using network theory methods, we studied chromatin interactions between broad domains and super enhancers in three ENCODE cell lines (K562, MCF7, GM12878) obtained via ChIA-PET, Hi-C, and Hi-CHIP assays. In these networks, broad domains and super enhancers interact more frequently with each other compared to their typical counterparts. Network measures and graphlets revealed distinct connectivity patterns associated with these regulatory elements that are robust across cell types and alternative assays. Machine learning models showed that these connectivity patterns could effectively discriminate broad domains from typical promoters and super enhancers from typical enhancers. Finally, targets of broad domains in these networks were enriched in disease-causing SNPs of cognate cell types. Taken together these results suggest a robust and unique organization of the chromatin around broad domains and super enhancers: loci critical for pathologies and cell-specific functions.