Can someone explain in simple terms to me what a directed acyclic graph is?

Question

Can someone explain in simple terms to me what a directed acyclic graph is? I have looked on Wikipedia but it doesn\'t really make me see its use in programming.

Answer 1

Several answers have given examples of the use of graphs (e.g. network modeling) and you've asked "what does this have to do with programming?".

The answer to that sub-question is that it doesn't have much of anything to do with programming. It has to do with problem solving.

Just like linked-lists are data structures used for certain classes of problems, graphs are useful for representing certain relationships. Linked lists, trees, graphs, and other abstract structures only have a connection to programming in that you can implement them in code. They exist at a higher level of abstraction. It's not about programming, it's about applying data structures in the solution of problems.

Answer 2

dots with lines pointing to other dots

Answer 3

I see lot of answers indicating the meaning of DAG (Directed Acyclic Graph) but no answers on its applications. Here is a very simple one -

Pre-requisite graph - During an engineering course every student faces a task of choosing subjects that follows requirements such as pre-requisites. Now its clear that you cannot take a class on Artificial Intelligence[B] without a pre requisite course on Algorithms[A]. Hence B depends on A or in better terms A has an edge directed to B. So in order to reach Node B you have to visit Node A. It will soon be clear that after adding all the subjects with its pre-requisites into a graph, it will turn out to be a Directed Acyclic Graph.

If there was a cycle then you would never complete a course :p

A software system in the university that allows students to register for courses can model subjects as nodes to be sure that the student has taken a pre-requisite course before registering for the current course.

My professor gave this analogy and it has best helped me understand DAG rather than using some complicated concept!

Another real time example -> Real Time example of how DAG's can be used in version system

Answer 4

A directed acyclic graph is useful when you want to represent...a directed acyclic graph! The canonical example is a family tree or genealogy.

Answer 5

graph = structure consisting of nodes, that are connected to each other with edges

directed = the connections between the nodes (edges) have a direction: A -> B is not the same as B -> A

acyclic = "non-circular" = moving from node to node by following the edges, you will never encounter the same node for the second time.

A good example of a directed acyclic graph is a tree. Note, however, that not all directed acyclic graphs are trees.

Answer 6

Directed Acyclic Graphs (DAG) have the following properties which distinguish them from other graphs:

1. Their edges show direction.
2. They don't have cycles.

Well, I can think of one use right now - DAG (known as Wait-For-Graphs - more technical details) are handy in detecting deadlocks as they illustrate the dependencies amongst a set of processes and resources (both are nodes in the DAG). Deadlock would happen when a cycle is detected.