In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated are the first and last vertices. A graph without cycles is called an acyclic graph.

**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.

how many cycles can a graph have? Actually a complete **graph has** exactly (n+1)! **cycles** which is O(nn).

Beside above, 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 DFS faster than BFS?

**BFS** is slower **than DFS**. **DFS** is more **faster than BFS**. **BFS** requires more memory compare to **DFS**. **DFS** require less memory compare to **BFS**.

### How can you tell if a directed graph is acyclic?

To test a graph for being acyclic: If the graph has no nodes, stop. The graph is acyclic. If the graph has no leaf, stop. The graph is cyclic. Choose a leaf of the graph. Go to 1. If the Graph has no nodes, stop. If the graph has no leaf, stop. Choose a leaf of Graph. Go to 1.

### How does topological sort determine cycle?

To detect cycle, we can check for a cycle in individual trees by checking back edges. To detect a back edge, we can keep track of vertices currently in recursion stack of function for DFS traversal. If we reach a vertex that is already in the recursion stack, then there is a cycle in the tree.

### What is the time complexity of BFS?

The Time complexity of BFS is O(V + E), where V stands for vertices and E stands for edges. The Time complexity of DFS is also O(V + E), where V stands for vertices and E stands for edges.

### Can undirected graphs have cycles?

An undirected graph is acyclic (i.e., a forest) if a DFS yields no back edges. Since back edges are those edges ( u , v ) connecting a vertex u to an ancestor v in a depth-first tree, so no back edges means there are only tree edges, so there is no cycle. So we can simply run DFS. If find a back edge, there is a cycle.

### Can tree edges form cycles?

(a) If v is an ancestor of u, then edge (u, v) is a back edge. We can use edge type information to learn some things about G. For example, tree edges form trees containing each vertex DFS visited in G. Also, G has a cycle if and only if DFS finds at least one back edge.

### How do you find the cycle of a graph using DFS?

Using DFS (Depth-First Search) Do DFS from every vertex. (please read DFS here). During DFS, for any current vertex ‘x’ (currently visiting vertex) if there an adjacent vertex ‘y’ is present which is already visited and ‘y’ is not a direct parent of ‘x’ then there is a cycle in graph.

### What is a cycle in a directed graph?

In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated are the first and last vertices. A graph without cycles is called an acyclic graph.

### What is simple cycle?

A simple cycle in a graph is a cycle with no repeated vertices (other than the requisite repetition of the first and last vertices). Note:That the length of a path or a cycle is its number of edges.

### Can a directed graph be disconnected?

Path in directed graphs is the same as in undirected graphs except that the path must go in the direction of the arrow. An undirected graph is called connected if there is a path between every pair of distinct vertices of the graph. An undirected graph that is not connected is called disconnected.

### What is directed graph with example?

A directed graph (or digraph) is a set of nodes connected by edges, where the edges have a direction associated with them. For example, an arc (x, y) is considered to be directed from x to y, and the arc (y, x) is the inverted link. Y is a direct successor of x, and x is a direct predecessor of y.

### What is a connected directed graph?

Connected Digraph. There are two distinct notions of connectivity in a directed graph. A directed graph is weakly connected if there is an undirected path between any pair of vertices, and strongly connected if there is a directed path between every pair of vertices (Skiena 1990, p. 173).

### What is directed and undirected graph?

A graph in which every edge is directed is called a Directed graph, and a graph in which every edge is undirected is called undirected graph.

### What is a weighted graph?

A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers (which are usually taken to be positive). SEE ALSO: Labeled Graph, Taylor’s Condition, Weighted Tree.

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