In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions. DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling).
Directed acyclic graphs are sometimes instead called acyclic directed graphs[1] or acyclic digraphs.[2]
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mathematics, particularly graph theory, and computer science, a directedacyclicgraph (DAG) is a directedgraph with no directed cycles. That is, it consists...
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since it is not transitive. The graph corresponding to the Levi graph of this generalization is a directedacyclicgraph. Consider, for example, the generalized...
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the graph. Removing these edges from the graph breaks all of the cycles, producing an acyclic subgraph of the given graph, often called a directed acyclic...
any directed cycle and therefore makes it into a directedacyclicgraph. Every graph has an acyclic orientation. The chromatic number of any graph equals...
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every edge belongs to a cycle Directedacyclicgraph, a directedgraph with no cycles Strongly connected graph, a directedgraph in which every edge belongs...
ordering is possible if and only if the graph has no directed cycles, that is, if it is a directedacyclicgraph (DAG). Any DAG has at least one topological...
describe either of two equivalent structures: a directedacyclicgraph (DAG) in which there is at most one directed path between any two vertices, or equivalently...
should have no cycles". This implies that the dependencies form a directedacyclicgraph. In this UML package diagram, package A depends on packages B and...
automatically using graph drawing techniques. The phrase "Hasse diagram" may also refer to the transitive reduction as an abstract directedacyclicgraph, independently...
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