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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.
Hebrew punctuation – Punctuation conventions of the Hebrew language over time; Glossary of mathematical symbols; Japanese punctuation; Korean punctuation; Ordinal indicator – Character(s) following an ordinal number (used of the style 1st, 2nd, 3rd, 4th or as superscript, 1 st, 2 nd, 3 rd, 4 th or (though not in English) 1º, 2º, 3º, 4º).
Graph coloring [2] [3]: GT4 Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph.
A valid schedule for the disjunctive graph may be obtained by finding an acyclic orientation of the undirected edges – that is, deciding for each pair of non-simultaneous tasks which is to be first, without introducing any circular dependencies – and then ordering the resulting directed acyclic graph. In particular, suppose that all tasks ...
Ancestral graphs are mixed graphs used with three kinds of edges: directed edges, drawn as an arrow from one vertex to another, bidirected edges, which have an arrowhead at both ends, and undirected edges, which have no arrowheads. It is required to satisfy some additional constraints:
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.
For example, in written English (or other languages using the Latin alphabet), there are two different physical representations of the lowercase Latin letter "a": "a" and "ɑ". Since, however, the substitution of either of them for the other cannot change the meaning of a word, they are considered to be allographs of the same grapheme, which ...