Linear algebraic depth-first search

There is a recent push by a segment of the graph community to implement graph algorithms in the language of linear algebra. However, graph algorithms that depend on depth-first search (DFS) techniques are often highlighted as limitations of the linear algebraic approach as linear algebraic formulation of DFS algorithms are few, if any. This paper provides a linear algebraic approach for developing DFS graph algorithms and demonstrates its use for defining three classical DFS-based computations: Binary tree traversal, topological sort, and biconnected components.