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In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs ), with each edge directed from one vertex to another, such that following those directions will never form a closed loop.
An alternative algorithm for topological sorting is based on depth-first search.The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node):
The DAG defines the dataflow of the application, and the vertices of the graph defines the operations that are to be performed on the data. The "computational vertices" are written using sequential constructs, devoid of any concurrency or mutual exclusion semantics.
A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. [2] A directed tree, [3] oriented tree, [4] [5] polytree, [6] or singly connected network [7] is a directed acyclic graph (DAG) whose underlying undirected graph is ...
A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). [1] While it is one of several forms of causal notation, causal networks are special cases of Bayesian ...
In graph theory, the cycle rank of a directed graph is a digraph connectivity measure proposed first by Eggan and Büchi ().Intuitively, this concept measures how close a digraph is to a directed acyclic graph (DAG), in the sense that a DAG has cycle rank zero, while a complete digraph of order n with a self-loop at each vertex has cycle rank n.
The number of acyclic orientations may be counted using the chromatic polynomial, whose value at a positive integer k is the number of k-colorings of the graph. Every graph G has exactly | χ G ( − 1 ) | {\displaystyle |\chi _{G}(-1)|} different acyclic orientations, [ 2 ] so in this sense an acyclic orientation can be interpreted as a ...
The comparability graph of a partial order is the undirected graph with a vertex for each element and an undirected edge for each pair of distinct elements x, y with either x ≤ y or y ≤ x. That is, it is formed from a minimal vertex series parallel graph by forgetting the orientation of each edge.