The EpiGRAPH web service http://epigraph.mpi-inf.mpg.de/ enables biologists to uncover hidden associations in vertebrate genome and epigenome datasets. Users can upload sets of genomic regions and EpiGRAPH will test multiple attributes (including DNA sequence, chromatin structure, epigenetic modifications and evolutionary conservation) for enrichment or depletion among these regions. Furthermore, EpiGRAPH learns to predictively identify similar genomic regions. This paper demonstrates EpiGRAPH's practical utility in a case study on monoallelic gene expression and describes its novel approach to reproducible bioinformatic analysis.