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.
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