Eulerian Melodies: Graph Algorithms for Music Composition

Graph-theoretic concepts, specifically Eulerian paths, can be used for algorithmic music composition. A Eulerian path is a walk through a graph that visits every edge exactly once, as illustrated by the classic Seven Bridges of Königsberg problem. This principle can be applied to fragment assembly problems, such as piecing together DNA sequences using de Bruijn graphs. The same approach is used to assemble musical motifs into a complete melody by finding a Eulerian path in a graph where nodes represent musical fragments, with a full Python implementation provided.