### Study on the Super Eulerian Path and the Sequence Reconstruction

#### Abstract

De Bruijn graph and Eulerian path in graph are useful mathematics tools for sequence representation and sequence analysis. In this paper, a weighted De Bruijn graph is first proposed. Each vertex and each edge of the graph is assigned a weight respectively. Then, a super Eulerian path in the weighted De Bruijn graph and its reconstruction algorithm from the weighted De Bruijn graph are proposed. The super Eulerian path is a path which can visit a vertex or a edge multiple times. This work is useful for solving the repetitive region problem of the DNA reconstruction.

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