In specific cases, chromatin clearly forms long-range loops that place distant regulatory elements in close proximity to transcription start sites, but we have limited understanding of many loops identified by Chromosome Conformation Capture (such as Hi-C) analyses. In efforts to elucidate their characteristics and functions, we have identified highly interacting regions (HIRs) using intra-chromosomal Hi-C datasets with a new computational method based on looking at the eigenvector that corresponds to the smallest eigenvalue (here unity). Analysis of these regions using ENCODE data shows that they are in general enriched in bound factors involved in DNA damage repair and have actively transcribed genes. However, both highly transcribed regions as well as transcriptionally inactive regions can form HIRs. The results also indicate that enhancers and super-enhancers in particular form long-range interactions within the same chromosome. The accumulation of DNA repair factors in most identified HIRs suggests that protection from DNA damage in these regions is essential for avoidance of detrimental rearrangements.