| 释义 |
▪ I. graph, n.1|grɑːf, -æ-|
[Orig. an abbreviation of graphic formula: see graphic.]
1. A kind of symbolic diagram (used in Chemistry, Mathematics, etc.) in which a system of connexions is expressed by spots or circles, some pairs of which are colligated by one or more lines. Also, occas. the system expressed by one of these diagrams. In abstract terms: A finite, non-empty set of elements together with a set (empty or non-empty) of unordered pairs of these elements.
‘Graphs’ were first employed (under the name of ‘graphic formulæ’: see graphic a. 5) in Chemistry for expressing the relations of the elements forming a compound. The application to Mathematics (app. also the shortened name) is due to Sylvester.
1878Sylvester in Amer. Jrnl. Math. I. 65 The graph to nitric anhydride. Ibid. 79 Chemical graphs..are to be regarded as mere translations into geometrical forms of trains of priorities and sequences having their proper habitat in the sphere of order. Ibid. 126 note, Whilst I was only able, in certain cases, to represent in terms of the roots of the parent quantic, the quantitative constitution of a form pictured by a graph..he [Clifford]..has found the universal pass key to the quantification of graphs. 1879Proc. Lond. Math. Soc. XI. 2 On Clifford's Graphs..Dr. Spottiswoode. 1884Amer. Jrnl. Math. VI. 382 The Method of Graphs applied to Compound Partitions. 1931Proc. Nat. Acad. Sci. XVII. 122 Suppose we assign to each vertex of a graph a color in such a way that each pair of vertices joined by an arc are of different colors. 1966McGraw-Hill Encycl. Sci. & Technol. VI. 255/2 If points represent people and lines their interrelationships, then a graph may be used to depict the structure of a social group. 1967H. C. Sneyd tr. Kaufmann's Graphs i. 10 The map of all the roads in a country..forms a graph. 1969F. Harary Proof Techniques in Graph Theory i. 1 By far the most celebrated problem concerning graphs is the Four Color Conjecture. 1971W. L. Price Graphs & Networks i. 1 Many problems of sequencing and scheduling can be looked upon as problems in graph and network theory. Ibid. ii. 7 If the set A is empty and the graph consists only of nodes, the result is called a null graph.
2. Alg. A graphical representation of the locus of a function; the traced curve of an equation. In wider use: A line or curve representing the variation of one quantity with another, each quantity being measured along one of a pair of axes at right angles.
1886Chrystal Algebra i. 307 The representative point will therefore trace out a continuous curve..This curve we may call the graph of the function. Ibid. 380 Draw the graphs of the two functions 3x - 5 and 5x + 7. 1926Encycl. Brit. III. 643 (caption) Graph showing consumption per head of tea and sugar in the United Kingdom in each year 1864–1913. 1951Roberts & Miller Heat & Thermodynamics (ed. 4) v. 155 The graph of entropy as a function of magnetic temperature is obtained by plotting this temperature against the calculated change of entropy. 1962A. R. W. Hayes Revision Physics i. 27 For a wire subjected to a stretching force four points on the load-extension graph can be distinguished. 1963L. Nobles in H. M. Burlage et al. Physical & Techn. Pharm. ii. 63 The plotting of a graph will establish quickly the meaning of a set of experimental data. 1971Nature 24 Sept. 271/1 These data are easier to comprehend in the form of a graph (Fig. 1).
3. Special Comb.: graph theory, the mathematical theory of the properties and applications of graphs (sense 1); hence graph-theoretic a.
1959Jrnl. Math & Physics XXXVIII. 104 (heading) A *graph theoretic method for the complete reduction of a matrix with a view toward finding its eigen values. 1973Nature 6 July 60/1 In some papers..numerical analysis and operations research are investigated from a graph theoretic point view, whilst in others computing techniques are applied to graph-theoretic problems.
1953Harary & Norman Graph Theory as Math. Model in Social Sci. p. iv, It soon became apparent that a whole cluster of substantive problems in psychology and sociology may be treated fruitfully by a branch of mathematics known as ‘*graph theory’. 1964Sci. Amer. Apr. 126/2 Today graph theory is a flourishing field. It is usually considered a branch of topology (because in most cases only the topological properties of graphs are considered). 1977B. Andrásfai Introductory Graph Theory v. 113 The degree of each vertex of G is k1 + k2 +..km and, similarly, the degree of the product of some polynomials is also equal to the sum of the degrees of the factors. This similarity illustrates a strong connection between algebra and graph theory.
▪ II. graph, n.2 colloq.|grɑːf, -æ-|
[Abstracted from chromograph, hectograph, etc.]
An apparatus of the nature of the chromograph, hectograph, etc., for taking copies of writing by pressing it on a gelatinous surface.
1884Advt., The Cyclostyle. No press, no washing, no graph.
▪ III. graph, n.3 Philol.|grɑːf, -æ-|
[ad. Gr. γραϕή writing; cf. digraph1.]
A visual symbol representing a phoneme or a segment or feature of speech; esp., a letter, or one of its occurrent forms, or a combination of letters.
1933Bloomfield Lang. xvii. 294 For the writers, the gh was now a mere silent graph, indicative only of vowel-quantity. 1953Medium ævum XXII. 14 The Exeter Book has one example of a clear t-graph where a 3 would normally be expected. 1958C. F. Hockett Course in Mod. Ling. lxii. 544 In Egypt certain graphs very early came to represent syllables rather than morphemes. 1968English Studies XLIX. 513 The graphs t and d in post-stress, intervocalic position can be ambiguous. 1970A. Cameron et al. Computers & O.E. Concordances 49 In the final printout, a simple graphic accommodation was employed to designate..the Old English graphs, ash, eth, and thorn.
▪ IV. graph, v.1 Math.|grɑːf, -æ-|
[ad. Gr. γράϕ-ειν to write.]
trans. To trace (a curve) from its equation; to trace the curve corresponding to (a given equation). Also fig. Hence ˈgraphing vbl. n.
1898Perry Applied Mechanics 21 Students will do well to graph on squared paper some curves like the following. Ibid. 2. Graph y = a + bx. Ibid. 1 The graphing of functions on squared paper. 1951M. McLuhan Mech. Bride 79/1 When producers want to know what the public wants, they graph it as curves. 1964Listener 20 Aug. 280/1 The book graphs and annotates the hostility between generations..and this is shaming to read. 1966I. Jefferies House Surgeon iii. 31 Anybody graph the survival rates against the day of admission?
▪ V. graph, v.2 colloq.|grɑːf, -æ-|
[f. graph n.2]
trans. To reproduce in a number of copies by means of a ‘graph’. Also absol.
1880Stationer XXXV. 3 We graphed by the dozen. 1894Westm. Gaz. 4 July 8/1 The Matabeleland News..is ‘graphed’ in manuscript. |