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Mixed graphs are also used as graphical models for Bayesian inference. In this context, an acyclic mixed graph (one with no cycles of directed edges) is also called a chain graph. The directed edges of these graphs are used to indicate a causal connection between two events, in which the outcome of the first event influences the probability of ...
A mixed graph is a graph in which some edges may be directed and some may be undirected. It is an ordered triple G = (V, E, A) for a mixed simple graph and G = (V, E, A, ϕ E, ϕ A) for a mixed multigraph with V, E (the undirected edges), A (the directed edges), ϕ E and ϕ A defined as above. Directed and undirected graphs are special cases.
A multigraph with multiple edges (red) and several loops (blue). Not all authors allow multigraphs to have loops. In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges [1]), that is, edges that have the same end nodes.
This mixed graph is Eulerian. The graph is even but not symmetric which proves that evenness and symmetricness are not necessary and sufficient conditions for a mixed graph to be Eulerian. All mixed graphs that are both even and symmetric are guaranteed to be Eulerian. However, this is not a necessary condition, as it is possible to construct a ...
The GraphML file format results from the joint effort of the graph drawing community to define a common format for exchanging graph structure data. It uses an XML-based syntax and supports the entire range of possible graph structure constellations including directed, undirected, mixed graphs, hypergraphs, and application-specific attributes. [1]
UML class diagram of a Graph (abstract data type) The basic operations provided by a graph data structure G usually include: [1] adjacent(G, x, y): tests whether there is an edge from the vertex x to the vertex y; neighbors(G, x): lists all vertices y such that there is an edge from the vertex x to the vertex y;
The NIST Dictionary of Algorithms and Data Structures [1] is a reference work maintained by the U.S. National Institute of Standards and Technology. It defines a large number of terms relating to algorithms and data structures. For algorithms and data structures not necessarily mentioned here, see list of algorithms and list of data structures.
The tabular representation lends itself well to computational applications. There are different ways to store graphs in a computer system. The data structure used depends on both the graph structure and the algorithm used for manipulating the graph. Theoretically one can distinguish between list and matrix structures but in concrete ...