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圖嵌入


CubicalGraphEmbeddings

圖嵌入,有時也稱為圖繪製,是 的一種特定畫法。圖嵌入最常在平面上繪製,但也可以在三個或更多維度中構建。上圖顯示了 立方體圖 的幾種嵌入方式。最常見的圖嵌入通常是 直線嵌入,其中所有邊都繪製為直線段。

CubicalGraphCircular

對嵌入的良好選擇可以產生特別具有啟發性的圖表。例如,立方體圖 的圓形(左側)嵌入說明了該圖固有的對稱性。

GraphEmbeddings

Skiena (1990) 考慮了多種不同型別的嵌入,包括 圓形、分級、放射狀、根和彈簧。圖嵌入可以在 Wolfram 語言 中使用以下選項在二維中視覺化GraphLayout. 或者,GraphPlot[g] 可以在二維中使用,以及GraphPlot3D[g] 在三維中使用。樹的嵌入可以使用以下方法視覺化TreePlot[g]。

Hong 和 Eades (2003) 給出了一種線性時間演算法,用於繪製具有最大對稱性的 不連通 平面圖。Freivalds 等人 (2002) 給出了一種基於 多格骨牌 填充的嵌入 不連通圖 的演算法。

Wolfram 語言中提供了許多圖的某些型別的預計算嵌入,如GraphData[g,"Graph", type]。


另請參閱

圓形嵌入, 嵌入, 積分嵌入, 平面嵌入, 平面直線嵌入, 直線交叉數, 直線嵌入, 單位距離圖

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參考文獻

Chung, F.; Leighton, T.; and Rosenberg, A. "Embeddings Graphs in Books: A Layout Problem with Applications to VLSI Design." SIAM J. Algebraic Disc. Meth. 8, 33-58, 1987.Di Battista, G.; Eades, P.; Tamassia, R.; and Tollis, I. G. Graph Drawing: Algorithms for the Visualization of Graphs. Englewood Cliffs, NJ: Prentice-Hall, 1998.Di Battista, G.; Garg, A.; Liotta, G.; Tamassia, R.; Tassinari, E.; and Vargiu, F. "An Experimental Comparison of Four Graph Drawing Algorithms." Computational Geom. 7, 303-325, 1997.Eades, P. "A Heuristic for Graph Drawing." Congr. Numer. 42, 149-160, 1984.Eades, P.; Fogg, I.; and Kelly, D. SPREMB: A System for Developing Graph Algorithms. Technical Report. Department of Computer Science. St. Lucia, Queensland, Australia: University of Queensland, 1988.Eades, P. and Tamassia, R. "Algorithms for Drawing Graphs: An Annotated Bibliography." Technical Report CS-89-09. Department of Computer Science. Providence, RI: Brown University, Feb. 1989.Freivalds, K.; Dogrusoz, U.; and Kikusts, P. "Disconnected Graph Layout and the Polyomino Packing Approach." In Graph Drawing: 9th International Symposium, GD 2001 Vienna, Austria, September 23-26, 2001, Revised Papers (Ed. P. Mutzel, M. Jünger, and S. Leipert). Berlin: Springer, pp. 378-391, 2002.Hong, S.-H. and Eades, P. "Symmetric Layout of Disconnected Graphs." In Algorithms and Computation: 14th International Symposium, ISAAC 2003, Kyoto, Japan, December 15-17, 2003, Proceedings (Ed. T. Ibaraki, N. Katoh, and H. Ono). Berlin: Springer, pp. 405-414, 2003.Kamada, T. and Kawai, S. "An Algorithm for Drawing General Undirected Graphs." Inform. Processing Lett. 31, 7-15, 1989.Malitz, S. M. "Genus g Graphs Have Pagenumber O(sqrt(g))." In Proc. 29th Sympos. Found. Computer Sci. IEEE Press, pp. 458-468, 1988.Pemmaraju, S. and Skiena, S. Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Cambridge, England: Cambridge University Press, 2003.Reingold, E. and Tilford, J. "Tidier Drawings of Trees." IEEE Trans. Software Engin. 7, 223-228, 1981.Skiena, S. "Graph Embeddings." §3.3 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 81 and 98-118, 1990.Supowit, K. and Reingold, E. "The Complexity of Drawing Trees Nicely." Acta. Inform. 18, 377-392, 1983.Tamassia, R. "Graph Drawing." Ch. 21 in Handbook of Computational Geometry (Ed. J.-R. Sack and J. Urrutia). Amsterdam, Netherlands: North-Holland, pp. 937-971, 2000.Vaucher, J. "Pretty Printing of Trees." Software Pract. Experience 10, 553-561, 1980.Wetherell, C. and Shannon, A. "Tidy Drawings of Trees." IEEE Trans. Software Engin. 5, 514-520, 1979.White, A. T. "Imbedding Problems in Graph Theory." Ch. 6 in Graphs of Groups on Surfaces: Interactions and Models (Ed. A. T. White). Amsterdam, Netherlands: Elsevier, pp. 49-72, 2001.

在 中被引用

圖嵌入

請引用為

Weisstein, Eric W. "圖嵌入。" 來自 --一個 Wolfram 網路資源。 https://mathworld.tw/GraphEmbedding.html

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