TRANSITIVE CLOSURE Meaning and
Definition
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Transitive closure is a concept in graph theory that refers to the process of determining the complete set of directed connections or relationships between all pairs of vertices in a directed graph. It involves identifying the indirect connections that exist between vertices, in addition to the direct connections already available.
In a directed graph, a connection between two vertices is considered to be direct if there is a direct edge or path between them. However, the transitive closure aims to find all possible connections between vertices, including those that require multiple intermediate steps to reach.
The transitive closure of a directed graph is often represented by a matrix, called the transitive closure matrix, where the entry at position (i, j) is 1 if there exists a path from vertex i to vertex j, and 0 otherwise. The process of determining the transitive closure involves applying the Warshall's algorithm or the Floyd-Warshall algorithm, both of which iteratively update the matrix until all indirect connections have been found.
The transitive closure has important applications in various fields, such as computer science, social networks, and transportation systems. It provides insights into the network structure, connectivity, and reachability of vertices in a directed graph. By revealing the complete set of relationships between vertices, the transitive closure assists in analyzing the characteristics and behavior of complex systems represented by graphs.
Common Misspellings for TRANSITIVE CLOSURE
- rransitive closure
- fransitive closure
- gransitive closure
- yransitive closure
- 6ransitive closure
- 5ransitive closure
- teansitive closure
- tdansitive closure
- tfansitive closure
- ttansitive closure
- t5ansitive closure
- t4ansitive closure
- trznsitive closure
- trsnsitive closure
- trwnsitive closure
- trqnsitive closure
- trabsitive closure
- tramsitive closure
- trajsitive closure
- trahsitive closure
Etymology of TRANSITIVE CLOSURE
The word "transitive closure" is a combination of two terms: "transitive" and "closure".
The term "transitive" comes from the Latin word "transitus", meaning "to cross over" or "to pass through". In mathematics and logic, transitivity refers to a relationship or property that holds when a variable or element passes from one state to another. More specifically, it refers to an attribute of relationships where if there is a connection or link between two elements (A and B), and another connection between elements B and C, then there is also a connection between elements A and C. This idea of transitivity can be found in various fields, such as set theory, graph theory, and formal logic.
The term "closure" in mathematics generally refers to an operation or property that guarantees that certain conditions are satisfied.
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