Examples of Digraphs:
1. Real-World Examples:
* Road Networks: Roads with one-way directions form a digraph, where cities are nodes and roads are directed edges.
* Airline Routes: Airlines connecting cities form a digraph, where cities are nodes and flights are directed edges.
* Website Links: Hyperlinks between webpages create a digraph, where pages are nodes and links are directed edges.
* Social Networks: Relationships in social networks can be represented as a digraph, where people are nodes and "following" or "friend" relationships are directed edges.
* Food Webs: The flow of energy in an ecosystem can be represented as a digraph, where organisms are nodes and predator-prey relationships are directed edges.
* Dependencies in Software: The dependencies between different parts of a software system can be represented as a digraph, where code modules are nodes and dependencies are directed edges.
* Flowchart of a Program: The flow of control in a program can be visualized as a digraph, where program steps are nodes and control flow is represented by directed edges.
2. Abstract Examples:
* Directed Acyclic Graphs (DAGs): Used for representing dependencies, project planning, and data flow.
* Finite State Machines (FSMs): Used for modeling systems with discrete states and transitions, like vending machines or traffic lights.
* Decision Trees: Used for classifying data, where each node represents a decision and each edge represents a possible outcome.
* Graphs with Cyclic Dependencies: Representing recursive relationships or feedback loops.
3. Mathematical Examples:
* Adjacency Matrix: A matrix where each row and column represents a node, and the entry at position (i, j) represents the weight of the edge from node i to node j.
* Adjacency List: A list where each element represents a node and contains a list of its outgoing edges.
These are just a few examples of the many ways digraphs are used in various fields. They are a powerful tool for representing relationships between objects and understanding the flow of information, energy, or control.