A directed acyclic graph is a directed graph that has
no cycles
. A vertex v of a directed graph is said to be reachable from another vertex u when there exists a path that starts at u and ends at v.
Is a directed graph cyclic?
Directed graphs have edges that point from one vertex to another. One can only go one direction on an edge. Non-directed / bidirectional graphs have edges where you can go back and forth between vertices.
Cyclic graphs are graphs with cycles
.
How do you determine if a given directed graph has a cycle?
There is a cycle in a graph
only if there is a back edge present in the graph
. A back edge is an edge that is joining a node to itself (self-loop) or one of its ancestor in the tree produced by DFS.
Can a DAG have back edge?
A digraph is
a DAG if there is no back-edge present in the graph
. Recall that a back-edge is an edge from a vertex to one of its ancestors in the DFS tree. Fact: For an edge u —> v in a directed graph, an edge is a back edge if departure[u] < departure[v] .
Can a simple graph have cycles?
A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex. In other words
a simple graph is a graph without loops
and multiple edges.
What is a directed cycle?
A directed cycle is simply
a cycle in a directed graph in which each edge is traversed in the same direction
. If we think about directed edges as one-way streets, then a directed cycle is simply a walk through the graph that returns to the original node and travels down each street in the legal direction.
Is a graph a cycle?
| Cycle graph | A cycle graph of length 6 | Vertices n | Edges n | Girth n |
|---|
What does it mean if a graph is cyclic?
A cyclic graph is
a graph containing at least one graph cycle
. A graph that is not cyclic is said to be acyclic. A cyclic graph possessing exactly one (undirected, simple) cycle is called a unicyclic graph.
What’s a cycle in a graph?
In graph theory,
a path that starts from a given vertex and ends at the same vertex
is called a cycle.
How many cycles does a graph have?
A graph containing no cycles of any length is known as an acyclic graph, whereas a graph containing
at least one cycle is called a cyclic graph
. A graph possessing exactly one (undirected, simple) cycle is called a unicyclic graph.
Can BFS detect cycle?
BFS wont work for a directed graph in finding cycles
. Consider A->B and A->C->B as paths from A to B in a graph. BFS will say that after going along one of the path that B is visited. When continuing to travel the next path it will say that marked node B has been again found,hence, a cycle is there.
Can DFS detect cycle?
Using a Depth First Search (DFS) traversal algorithm we can detect cycles in a directed graph
. If there is any self-loop in any node, it will be considered as a cycle, otherwise, when the child node has another edge to connect its parent, it will also a cycle.
Can a directed graph be disconnected?
An edgeless graph with two or more vertices is disconnected.
A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph
.
Can a directed graph have no edges?
Oriented graphs are directed graphs having no bidirected edges
(i.e. at most one of (x, y) and (y, x) may be arrows of the graph). It follows that a directed graph is an oriented graph if and only if it hasn’t any 2-cycle.
Can a DAG have cycles?
A directed acyclic graph is a directed graph that has no cycles
. A vertex v of a directed graph is said to be reachable from another vertex u when there exists a path that starts at u and ends at v.
How do you tell if a graph has a simple cycle?
A simple cycle is a cycle in a Graph with no repeated vertices (except for the beginning and ending vertex). Basically,
if a cycle can’t be broken down to two or more cycles
, then it is a simple cycle.
Can a path be a cycle?
Cycle is a closed path
. These can not have repeat anything (neither edges nor vertices). Note that for closed sequences start and end vertices are the only ones that can repeat.
Is loop a cycle?
A loop is commonly defined as an edge (or directed edge in the case of a digraph) with both ends as the same vertex. (For example from a to itself).
Although loops are cycles, not all cycles are loops
.
How do you tell if a graph is directed?
If you are able to find edge of opposite direction for each edge in your list, you can treat your graph as undirected (or directed with 2 opposite directed edges per pair of connected nodes). Otherwise, it is directed. (considering example above, if for vertex b there is no vertex a in its adjacent vertices list).
How do you know if a graph is complete?
A simple graph with ‘n’ mutual vertices is called a complete graph and it is denoted by ‘K
n
‘. In the graph, a vertex should have edges with all other vertices, then it called a complete graph. In other words,
if a vertex is connected to all other vertices in a graph, then it is called a complete graph
.
How do you implement a directed graph?
- Add a node to the graph.
- Create an edge between any two nodes.
- Check if a node exists in the graph.
- Given a node, return it’s neighbors.
- Return a list of all the nodes in the graph.
- Return a list of all edges in the graph.
What is difference between cycle graph and Chronocyclegraph?
Chronocycle Graph:
The Chronocycle graph is special form of cycle graph in which the light source is suitably interrupted so that the path appears as a series of pear-shaped dots the pointed end indicating the direction of movement and the spacing indicating the speed of movement.
