Structural variation (SV) is a class of genetic diversity whose importance is increasingly revealed by genome resequencing, especially with long-read technologies. One crucial problem when analyzing and comparing SVs in several individuals is their accurate genotyping, that is determining whether a described SV is present or absent in one sequenced individual, and if present, in how many copies. There are only a few methods dedicated to SV genotyping with long-read data, and all either suffer of a bias toward the reference allele by not representing equally all alleles, or have difficulties genotyping close or overlapping SVs due to a linear representation of the alleles. We present SVJedi-graph, a novel method for SV genotyping that relies on a variation graph to represent in a single data structure all alleles of a set of SVs. The long reads are mapped on the variation graph and the resulting alignments that cover allele-specific edges in the graph are used to estimate the most likely genotype for each SV. Running SVJedi-graph on simulated sets of close and overlapping deletions showed that this graph model prevents the bias toward the reference alleles and allows maintaining high genotyping accuracy whatever the SV proximity, contrary to other state of the art genotypers. On the human gold standard HG002 dataset, SVJedi-graph obtained the best performances, genotyping 99.5% of the high confidence SV callset with an accuracy of 95% in less than 30 min. SVJedi-graph is distributed under an AGPL license and available on GitHub at https://github.com/SandraLouise/SVJedi-graph and as a BioConda package.