Analysis of splice variants from short read RNA-seq data remains a challenging problem. Here we present a novel method for the genome-guided prediction and quantification of splice events from RNA-seq data, which enables the analysis of unannotated and complex splice events. Splice junctions and exons are predicted from reads mapped to a reference genome and are assembled into a genome-wide splice graph. Splice events are identified recursively from the graph and are quantified locally based on reads extending across the start or end of each splice variant. We assess prediction accuracy based on simulated and real RNA-seq data, and illustrate how different read aligners (GSNAP, HISAT2, STAR, TopHat2) affect prediction results. We validate our approach for quantification based on simulated data, and compare local estimates of relative splice variant usage with those from other methods (MISO, Cufflinks) based on simulated and real RNA-seq data. In a proof-of-concept study of splice variants in 16 normal human tissues (Illumina Body Map 2.0) we identify 249 internal exons that belong to known genes but are not related to annotated exons. Using independent RNA samples from 14 matched normal human tissues, we validate 9/9 of these exons by RT-PCR and 216/249 by paired-end RNA-seq (2 x 250 bp). These results indicate that de novo prediction of splice variants remains beneficial even in well-studied systems. An implementation of our method is freely available as an R/Bioconductor package [Formula: see text].