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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.
Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem. [3]: ND25, ND27 Clique cover problem [2] [3]: GT17
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 mixed Chinese postman problem (MCPP or MCP) is the search for the shortest traversal of a graph with a set of vertices V, a set of undirected edges E with positive rational weights, and a set of directed arcs A with positive rational weights that covers each edge or arc at least once at minimal cost. [1]
A geometric graph is a graph in which the vertices or edges are associated with geometric objects. Examples include Euclidean graphs, the 1-skeleton of a polyhedron or polytope, unit disk graphs, and visibility graphs. Topics in this area include: Graph drawing; Polyhedral graphs; Random geometric graphs; Voronoi diagrams and Delaunay ...
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.
A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example, if a graph represents a road network, the weights could represent the length of each road.