|
In mathematics, and more specifically in graph theory, a graph is a representation of a set of objects where some pairs of objects are connected by links. The interconnected objects are represented by mathematical abstractions called ''vertices'' (also called ''nodes'' or ''points''), and the links that connect some pairs of vertices are called ''edges'' (also called ''arcs'' or ''lines''). Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this is an undirected graph, because if person A shook hands with person B, then person B also shook hands with person A. In contrast, if there is an edge from person A to person B when person A knows of person B, then this graph is directed, because knowledge of someone is not necessarily a symmetric relation (that is, one person knowing another person does not necessarily imply the reverse; for example, many fans may know of a celebrity, but the celebrity is unlikely to know of all their fans). The former type of graph is called an ''undirected graph'' and the edges are called ''undirected edges'' while the latter type of graph is called a ''directed graph'' and the edges are called ''directed edges''. Graphs are the basic subject studied by graph theory. The word "graph" was first used in this sense by J. J. Sylvester in 1878.〔See: * J. J. Sylvester (February 7, 1878) ("Chemistry and algebra," ) ''Nature'', ''17'' : 284. From page 284: "Every invariant and covariant thus becomes expressible by a ''graph'' precisely identical with a Kekuléan diagram or chemicograph." * J. J. Sylvester (1878) ("On an application of the new atomic theory to the graphical representation of the invariants and covariants of binary quantics, — with three appendices," ) ''American Journal of Mathematics, Pure and Applied'', ''1'' (1) : 64-90. The term "graph" first appears in this paper on page 65.〕 ==Definitions== Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Graph (mathematics)」の詳細全文を読む スポンサード リンク
|