An algorithm for drawing general undirected graphs.

*(English)*Zbl 0679.68128From the author’s introduction: “We present a simple but successful algorithm for drawing undirected graphs and weighted graphs. The basic idea of our algorithm is as follows. We regard the desirable “geometric” (Euclidean) distance between two vertices in the drawing as the “graph theoretic” distance between them in the corresponding graph. We introduce a virtual dynamic system in which every two vertices are connected by a “spring” of such desirable length. Then, we regard the optimal layout of vertices as the state in which the total spring energy of the system is minimal.”

##### MSC:

68R10 | Graph theory (including graph drawing) in computer science |

68P05 | Data structures |

68U99 | Computing methodologies and applications |

##### Software:

Algorithm 97
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\textit{T. Kamada} and \textit{S. Kawai}, Inf. Process. Lett. 31, No. 1, 7--15 (1989; Zbl 0679.68128)

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##### References:

[1] | Batini, C; Nardelli, E; Tamassia, R, A layout algorithm for data flow diagrams, IEEE trans. software eng., SE-12, 538-546, (1986) |

[2] | Becker, B; Hotz, G, On the optimal layout of planar graphs with fixed boundary, SIAM J. comput., 16, 946-972, (1987) · Zbl 0625.05020 |

[3] | Behzad, M; Chartrand, G; Lesniak-Foster, L, Graphs & diagraphs, (1979), Prindle, Weber & Schmidt Boston, MA |

[4] | Carpano, M, Automatic display of hierarchized graphs for computer-aided decision analysis, IEEE trans. syst., man, cybern., SMC-10, 705-715, (1980) |

[5] | Corneil, D.G; Gotlieb, C.C, An efficient algorithm for graph isomorphism, J. ACM, 17, 51-64, (1970) · Zbl 0199.27801 |

[6] | Eades, P, A heuristics for graph drawing, Congr. numer., 42, 149-160, (1984) |

[7] | Eades, P; Tamassia, R, Algorithms for drawing graphs: an annotated bibliography, () · Zbl 0804.68001 |

[8] | Floyd, R.W, Algorithm 97: shortest path, Comm. ACM, 5, 345, (1962) |

[9] | Hopcroft, J.E; Tarjan, R.E, A V log V algorithm for isomorphism of triconnected of planar graphs, J. comput. syst. sci., 7, 323-331, (1973) · Zbl 0274.05103 |

[10] | Kamada, T; Kawai, S, Automatic display of network structures for human understanding, () |

[11] | Lipton, R; North, S; Sandberg, J, A method for drawing graphs, Proc. ACM symposium on computational geometry, 153-160, (1985) |

[12] | Mittal, H.B, A fast backtrack algorithm for graph isomorphism, Inform. process. lett., 29, 105-110, (1988) · Zbl 0652.05023 |

[13] | Moffat, A; Takaoka, T, An all pairs shortest path algorithm with expected running time O(n2log n), Proc. conf. found. comp. sci., 101-105, (1985) |

[14] | Rowe, L.A; Davis, M; Messinger, E; Meyer, C; Spirakis, C; Tuan, A, A browser for directed graphs, Software pract. exper., 17, 61-76, (1987) |

[15] | Sedgewick, R, Algorithms, (1983), Addison-Wesley Reading, MA · Zbl 0529.68002 |

[16] | Spira, P.M, A new algorithm for finding all shortest paths in a graph of positive arcs in average time O(n2log2n), SIAM J. comput., 2, 28-32, (1973) · Zbl 0254.05118 |

[17] | Sugiyama, K, Achieving uniqueness requirement in drawing digraphs: optimum code algorithm and hierarchy isomorphism, () |

[18] | Sugiyama, K; Tagawa, S; Toda, M, Methods for visual understanding of hierarchical system structures, IEEE trans. syst. man, cybern., SMC-11, 109-125, (1981) |

[19] | Tamassia, R; Battista, G; Batini, C, Automatic graph drawing and readability of diagrams, IEEE trans. syst. man, cybern., SMC-18, 61-79, (1988) |

[20] | Tutte, W.T, How to draw a graph, Proc. London math. soc., 3, 743-768, (1963) · Zbl 0115.40805 |

[21] | Warfield, J.N, Crossing theory and hierarchy mapping, IEEE trans. syst. man, cybern., SMC-7, 505-523, (1977) · Zbl 0367.93004 |

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