What is the difference between a directed acyclic graph and a cyclic graph?

A directed acyclic graph (DAG) and a cyclic graph are two different types of graphs that differ in their structure and properties.

1. Directed Acyclic Graph (DAG):
- A DAG is a directed graph that does not contain any directed cycles.
- It means that there are no loops or cycles in the graph where you can traverse from a vertex and come back to the same vertex following the direction of the edges.
- In other words, it is impossible to start at any vertex and follow the directed edges to return to the same vertex without going through any vertex more than once.
- DAGs are commonly used in various applications, such as representing dependencies, scheduling tasks, and topological sorting.

2. Cyclic Graph:
- A cyclic graph, also known as a directed cyclic graph or simply a cycle, is a directed graph that contains at least one directed cycle.
- A directed cycle is a path in the graph that starts and ends at the same vertex, following the direction of the edges.
- In a cyclic graph, it is possible to traverse from a vertex and come back to the same vertex by following a directed path.
- Cyclic graphs can represent various scenarios, such as circular dependencies, feedback loops, and repetitive processes.

In summary, the main difference between a directed acyclic graph and a cyclic graph is the presence or absence of directed cycles. A DAG does not contain any directed cycles, while a cyclic graph contains at least one directed cycle.