A directed graph, also known as a digraph, is a type of graph where the edges connecting the nodes are directional, meaning they have a specific direction associated with them. In other words, it is a graph consisting of vertices or nodes connected by directed edges or arcs.
An example of a directed graph is a family tree. In a family tree, each person is represented by a node, and the directional edges show the relationships between them. For instance, the father node points to the mother node to depict marriage, and the parent nodes point to the children’s nodes to depict parent-child relationships. In this example, the edges are directional because the relationship between a parent and a child has a specified direction. Another example could be the relationship between cities, where the directed edges represent one-way streets or connections from one city to another.
Directed Graph is a graph whose edges are directed, which means that they have a direction assigned to them.
In a directed graph, each node has one or more edges pointing outwards, indicating the direction of the relationship between nodes.
Directed graph is used to represent a wide range of real-world applications such as social networks, flow networks, and web pages.
A directed graph can contain cycles, which can be defined as a sequence of nodes that lead back to the starting node.
The properties of directed graphs, such as connectivity and reachability, can be analyzed using algorithms such as Depth-First Search (DFS) and Breadth-First Search (BFS).
In a directed graph, the in-degree of a node corresponds to the number of edges coming into the node, while the out-degree refers to the number of edges pointing outwards from the node.
The shortest path between two nodes in a directed graph can be calculated using Dijkstra’s algorithm, Bellman-Ford algorithm, or Floyd-Warshall algorithm.
The complexity of algorithms for directed graphs can be higher compared to undirected graphs due to the added complexity of tracking the direction of edges.
What is a directed graph?
Answer: A directed graph is a type of graph where edges have a specific direction or orientation, and cannot be traversed in the opposite direction.
What is the degree of a vertex in a directed graph?
Answer: The degree of a vertex in a directed graph is the number of edges that are incident to it, taking into account their directions.
What is a path in a directed graph?
Answer: A path in a directed graph is a sequence of vertices that can be traversed by following the direction of the edges, starting from one vertex and ending at another.
What is a cycle in a directed graph?
Answer: A cycle in a directed graph is a path that starts and ends at the same vertex, and passes through at least one other vertex more than once.
What is a strongly connected component of a directed graph?
Answer: A strongly connected component of a directed graph is a subset of the vertices that can be reached from any other vertex in the same subset by following directed edges.