In graph theory, a loop (also called a self-loop or a "buckle") is an edge that connects a vertex to itself. A simple graph contains no loops. For an undirected graph, the degree of a vertex is equal to the number of adjacent vertices.
In graph theory, there are several different types of object called cycles; a closed walk and a simple cycle. A closed walk consists of a sequence of vertices starting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph.
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph, or set of nodes connected by edges, where the edges have a direction associated with them. In formal terms, a digraph is a pair (sometimes ) of:
In computer science, Kosaraju's algorithm (also known as the Kosaraju–Sharir algorithm) is a linear time algorithm to find the strongly connected components of a directed graph. Aho, Hopcroft and Ullman credit it to an unpublished paper from 1978 by S. Rao Kosaraju.
In graph theory, the strongly connected components of a directed graph may be found using an algorithm that uses depth-first search in combination with two stacks, one to keep track of the vertices in the current component and the second to keep track of the current search path.
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that are themselves strongly connected.
We apply DFS on the graph and keep track of two properties for each node in DFS tree produced :1. Its time(or order) of first being discovered in DFS.(say p1)2. The order of oldest ancestor it can reach.(say p2)Initially both are same for every node.
Tarjan's Algorithm is an algorithm in graph theory for finding the strongly connected components of a graph. Although proposed earlier, it can be seen as an improved version of Kosaraju's algorithm, and is comparable in efficiency to the path-based strong component algorithm.