In Graph Theory
In computer science, the concept of transitive closure can be thought of as constructing a data structure that makes it possible to answer reachability questions. That is, can one get from node a to node d in one or more hops? A binary relation tells you only that node a is connected to node b, and that node b is connected to node c, etc. After the transitive closure is constructed, as depicted in the following figure, in an O(1) operation one may determine that node d is reachable from node a. The data structure is typically stored as a matrix, so if matrix = 1, then it is the case that node 1 can reach node 4 through one or more hops.
The transitive closure of a directed acyclic graph (DAG) is the reachability relation of the DAG and a strict partial order.
Read more about this topic: Transitive Closure
Famous quotes containing the words graph and/or theory:
“When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”
—Marshall McLuhan (1911–1980)
“Psychotherapy—The theory that the patient will probably get well anyway, and is certainly a damned ijjit.”
—H.L. (Henry Lewis)