Graph connectivity | Graph invariants

Cycle rank

In graph theory, the cycle rank of a directed graph is a digraph connectivity measure proposed first by Eggan and Büchi. Intuitively, this concept measures how close adigraph is to a directed acyclic graph (DAG), in the sense that a DAG hascycle rank zero, while a complete digraph of order n with a self-loop ateach vertex has cycle rank n. The cycle rank of a directed graph is closely related to the tree-depth of an undirected graph and to the star height of a regular language. It has also found usein sparse matrix computations (see ) and logic. (Wikipedia).

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Related pages

Graph (discrete mathematics) | Connectivity (graph theory) | Nondeterministic finite automaton | Star height | Nested dissection | Regular language | Tree-depth | Cartesian product of graphs | Graph theory | Adjacency matrix | Set (mathematics) | Circuit rank | Complete graph | Concatenation | Sparse matrix | Approximation algorithm | Directed acyclic graph | Directed graph | International Colloquium on Automata, Languages and Programming