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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.
For most graphs, this transformation is not useful because it creates cycles of negative length in −G. But if G is a directed acyclic graph (DAG), then no negative cycles can be created, and a longest path in G can be found in linear time by applying a linear time algorithm for shortest paths in −G, which is also a directed acyclic graph. [4]
In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define each node to be a descendant of itself (so if v has a direct connection from w, w 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 ...
A directed graph is acyclic if it has no directed cycles. The usual name for such a digraph is directed acyclic graph (DAG). [7] Multitrees are DAGs in which there are no two distinct directed paths from the same starting vertex to the same ending vertex.
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 ...
DAG Abbreviation for directed acyclic graph, a directed graph without any directed cycles. deck The multiset of graphs formed from a single graph G by deleting a single vertex in all possible ways, especially in the context of the reconstruction conjecture. An edge-deck is formed in the same way by deleting a single edge in all possible ways.
Figure 1 is a causal graph that represents this model specification. Each variable in the model has a corresponding node or vertex in the graph. Additionally, for each equation, arrows are drawn from the independent variables to the dependent variables. These arrows reflect the direction of causation.