directed graph
each edge has direction
A directed graph is a mathematical structure that consists of a collection of nodes or vertices and a set of directed edges or arcs that connect these nodes. In a directed graph, each edge has a direction, indicating the direction of movement between the two vertices it connects.
Directed graphs are used to model a wide range of phenomena, such as traffic flows, social networks, electrical circuits, and biological pathways. They are also used in computer science and programming, including database systems, compiler design, and graph algorithms.
Some properties of directed graphs include:
– In-degree and out-degree: the in-degree of a node is the number of edges pointing towards it, while the out-degree is the number of edges pointing away from it.
– Reachability: a node is reachable from another node if there is a path of directed edges between them.
– Strongly connected components: a strongly connected component is a subgraph in which every node is reachable from every other node.
– Cycles: a cycle is a path in which the starting and ending nodes are the same, and there is at least one edge pointing back to a node in the path.
Directed graphs can be represented using various data structures, such as adjacency matrices or adjacency lists, which store information about the nodes and edges in the graph. They can also be visualized using graph drawing algorithms, which produce diagrams that show the nodes and edges and highlight different features of the graph.
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