Reformulating a Breadth-First Search Algorithm on an Undirected Graph in the Language of Linear Algebra

The formulation of algorithms from sparse linear algebra is often based on suitable concepts from graph theory. However, conversely, the formulation of algorithms from graph theory is rarely based on suitable concepts from sparse linear algebra. Here, we present an illustrating example of a standard graph algorithm that is expressed in the language of sparse linear algebra. More precisely, we reformulate a breadth-first search (BFS) algorithm on an undirected graph using sparse matrix-vector products. In addition, we demonstrate that the performance of this matrix-based BFS algorithm on an Intel Core 2 Duo CPU E8400 is improved as compared to a traditional graph-based BFS algorithm.