DIRECTED GRAPH Meaning and
Definition
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A directed graph, also known as a digraph, is a fundamental concept in mathematics and computer science. It is a mathematical structure that represents a collection of objects, where some pairs of objects are connected by directed edges.
In a directed graph, each object is referred to as a vertex or node, and the connections between them are represented by directed edges or arcs. These edges have a specific direction associated with them, indicating the flow or the relationship between the connected vertices. For example, if vertex A is connected to vertex B with a directed edge, it means that there is a directed path from A to B, but not necessarily from B to A.
Directed graphs are commonly used to model relationships, dependencies, or flow of information in various fields, including computer science, social sciences, and operations research. They provide a powerful way to represent complex systems and analyze their properties.
Unlike undirected graphs, which only have symmetric connections, directed graphs have directed edges that enable the representation of one-way relationships, making them particularly useful in situations where the direction of interactions is essential. Furthermore, directed graphs can also have cycles, where a sequence of edges leads back to the same vertex.
Overall, directed graphs are valuable tools for visualizing and analyzing complex relationships in a wide range of fields, making them a key concept in graph theory and computational modeling.
Etymology of DIRECTED GRAPH
The term "directed graph" is derived from the combination of the words "directed" and "graph".
The word "directed" comes from the verb "direct", which originates from the Latin word "dirigere". "Dirigere" combines the prefix "di-" meaning "apart" or "away" and the root "regere" meaning "to guide" or "to lead". Therefore, "directed" in the context of a graph refers to the presence of directed edges or arrows, indicating the flow or direction between the nodes.
The term "graph" has its roots in mathematics and comes from the Latin word "graphium" meaning "writing instrument" or "stylus". The modern usage of the word "graph" in mathematics was popularized by the Swiss mathematician Leonhard Euler in the 18th century.
