Graph Embedding
A graph embedding is a particular drawing of a graph. The above figure shows the first several circular embeddings of the cubical graph. The most commonly encountered graph embeddings are generally straight line drawings, in which all edges are drawn as straight line segments.
While the underlying object is independent of the embedding, a clever choice of embedding can lead to particularly illuminating diagrams. For example, the circular (left) embedding of the cubical graph illustrates this graph's inherent symmetries.
Skiena (1990) considers a number of different types of embeddings, including circular, ranked, radial, rooted, and spring. Graph embeddings can be visualized in the Wolfram Language in two dimensions using GraphPlot[g] and in three dimensions using GraphPlot3D[g]. Embeddings for trees can be visualized using TreePlot[g].
Precomputed embeddings of certain types for a number of graphs are available in the Wolfram Language as GraphData[g, "Images", type].
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.
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.
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 
."
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.
Weisstein, Eric W. "Graph Embedding." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GraphEmbedding.html
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