Genome graphs are emerging as an important novel approach to the analysis of high-throughput human sequencing data. By explicitly representing genetic variants and alternative haplotypes in a mappable data structure, they can enable the improved analysis of structurally variable and hyperpolymorphic regions of the genome. In most existing approaches, graphs are constructed from variant call sets derived from short-read sequencing. As long-read sequencing becomes more cost-effective and enables assembly for increasing numbers of whole genomes, a method for the direct construction of a genome graph from sets of assembled human genomes would be desirable. Such assembly-based genome graphs would encompass the wide spectrum of genetic variation accessible to long-read-based assembly, including large structural variants and divergent haplotypes. Here we present NovoGraph, a method for the construction of a human genome graph directly from a set of assemblies. NovoGraph constructs a genome-wide multiple sequence alignment of all input contigs and creates a graph by merging the input sequences at positions that are both homologous and sequence-identical. NovoGraph outputs resulting graphs in VCF format that can be loaded into third-party genome graph toolkits. To demonstrate NovoGraph, we construct a genome graph with 23,478,835 variant sites and 30,582,795 variant alleles from assemblies of seven ethnically diverse human genomes (AK1, CHM1, CHM13, HG003, HG004, HX1, NA19240). Initial evaluations show that mapping against the constructed graph reduces the average mismatch rate of reads from sample NA12878 by approximately 0.2%, albeit at a slightly increased rate of reads that remain unmapped.