FIG. 3.

The (approximate) paired de Bruijn graph: (a, b) The paired de Bruijn construction for k = 2, d = 4 from the same string S as in Fig. 1. In (a), the outer circle has an edge from every element of the (3, 4)-spectrum. (b) The paired de Bruijn graph after all the gluings; notice that it has only one branching vertex, versus four in the de Bruijn graph (Fig. 1d). (c–e) The construction of the approximate paired de Bruijn graph for k = 2, d = 5, Δ = 1. In (c), one possible covering spectrum is shown in the outside circle, with black edges for elements with mate pair distance 6 and blue edges for distance 5. Since Δ = 1, we glue vertices if they have equal left labels and their right labels are a distance at most 2 apart from each other in the de Bruijn graph (Fig. 1d). The final multigraph after all vertex gluings is shown in (d), and the resulting simple graph, used to spell the contigs, is shown in (e). Notice that this graph now has three branching vertices.