Efforts to incorporate human genetic variation into the reference human genome have converged on the idea of a graph representation of genetic variation within a species, a genome sequence graph. A sequence graph represents a set of individual haploid reference genomes as paths in a single graph. When that set of reference genomes is sufficiently diverse, the sequence graph implicitly contains all frequent human genetic variations, including translocations, inversions, deletions, and insertions. In representing a set of genomes as a sequence graph, one encounters certain challenges. One of the most important is the problem of graph linearization, essential both for efficiency of storage and access, and for natural graph visualization and compatibility with other tools. The goal of graph linearization is to order nodes of the graph in such a way that operations such as access, traversal, and visualization are as efficient and effective as possible. A new algorithm for the linearization of sequence graphs, called the flow procedure (FP), is proposed in this article. Comparative experimental evaluation of the FP against other algorithms shows that it outperforms its rivals in the metrics most relevant to sequence graphs.