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The yellow directed acyclic graph is the condensation of the blue directed graph. It is formed by contracting each strongly connected component of the blue graph into a single yellow vertex. Any directed graph may be made into a DAG by removing a feedback vertex set or a feedback arc set, a set of vertices or edges (respectively) that touches ...
Definition. In formal terms, a directed graph is an ordered pair G = (V, A) where [1] A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines. It differs from an ordinary or undirected graph, in that the latter is defined in terms of ...
A directed graph with three vertices (blue circles) and three edges (black arrows). In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of ...
DOT is a graph description language, developed as a part of the Graphviz project. DOT graphs are typically stored as files with the .gv or .dot filename extension — .gv is preferred, to avoid confusion with the .dot extension used by versions of Microsoft Word before 2007. [1] dot is also the name of the main program to process DOT files in ...
Graph. Worst-case performance. Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in linear time, matching the time bound for alternative methods including Kosaraju's algorithm and the path-based strong component algorithm.
Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Extra memory, usually a queue, is needed to keep track of the child nodes that were encountered ...
A directed graph. A classic form of state diagram for a finite automaton (FA) is a directed graph with the following elements (Q, Σ, Z, δ, q 0, F): [2] [3]. Vertices Q: a finite set of states, normally represented by circles and labeled with unique designator symbols or words written inside them
The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly once. The problem may specify the start and end of the path, in which case the starting vertex s and ending ...