Abstract
Graphs provide a versatile model for data from a large variety of application domains, for example, software engineering, telecommunication, and biology. Understanding the information that is represented by the graph is crucial for scientists and engineers to understand critical issues in these domains. Graph visualization is the process of creating a drawing of a graph so that a human can understand the graph. However, the depth of understanding depends on the quality of the graph representation. Good visualization can facilitate efficient visual analysis of the data to detect patterns and trends. Important aspects of the development of graph drawing methods are the efficiency and accuracy of the algorithms, and the quality of the resulting picture. In this chapter, we discuss the geometric properties of good graph visualizations as node-link diagrams, and describe methods for constructing good layouts of graphs.
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References
Angelini P, Binucci C, Lozzo GD, Didimo W, Grilli L, Montecchiani F, Patrignani M, Tollis IG (2013) Drawing non-planar graphs with crossing-free subgraphs. In: Wismath SK, Wolff A (eds) Graph drawing. In: 21st international symposium, GD 2013, Bordeaux, September 23–25, 2013. Revised selected papers. Lecture notes in computer science, vol 8242. Springer, Berlin, pp 292–303. http://dx.doi.org/10.1007/978-3-319-03841-4_26
Argyriou EN, Bekos MA, Kaufmann M, Symvonis A (2013) Geometric RAC simultaneous drawings of graphs. J Graph Algorithms Appl 17(1):11–34. http://dx.doi.org/10.7155/jgaa.00282
Arikushi K, Fulek R, Keszegh B, Moric F, Tóth CD (2012) Graphs that admit right angle crossing drawings. Comput Geom 45(4):169–177. http://dx.doi.org/10.1016/j.comgeo.2011.11.008
Auer C, Brandenburg FJ, Gleißner A, Reislhuber J (2015) 1-Planarity of graphs with a rotation system. J Graph Algorithms Appl 19(1):67–86. http://dx.doi.org/10.7155/jgaa.00347
Barnard ST, Simon HD (1994) Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. Concurrency Pract Experience 6(2):101–117. http://dx.doi.org/10.1002/cpe.4330060203
Bartel G, Gutwenger C, Klein K, Mutzel P (2010) An experimental evaluation of multilevel layout methods. In: Brandes U, Cornelsen S (eds) Graph drawing - 18th international symposium, GD 2010, Konstanz, September 21–24, 2010. Revised selected papers. Lecture notes in computer science, vol 6502, Springer, Berlin, pp 80–91. http://dx.doi.org/10.1007/978-3-642-18469-7_8
Batini C, Nardelli E, Tamassia R (1986) A layout algorithm for data flow diagrams. IEEE Trans Softw Eng 12(4):538–546. http://doi.ieeecomputersociety.org/10.1109/TSE.1986.6312901
Battista GD, Eades P, Tamassia R, Tollis IG (1999) Graph drawing: algorithms for the visualization of graphs. Prentice-Hall, Upper Saddle River
Biedl TC, Madden B, Tollis IG (1997) The three-phase method: a unified approach to orthogonal graph drawing. In: Battista GD (ed) (1997) Graph drawing. In: 5th international symposium, GD ’97, Rome, September 18–20, 1997, Proceedings. Lecture notes in computer science, vol 1353. Springer, Berlin, pp 391–402. http://dx.doi.org/10.1007/3-540-63938-1_84
Böttger J, Schurade R, Jakobsen E, Schäfer A, Margulies D (2014) Connexel visualization: a software implementation of glyphs and edge-bundling for dense connectivity data using brainGL. Front Neurosci 8:15. https://doi.org/10.3389/fnins.2014.00015
Boyer JM, Myrvold WJ (2004a) On the cutting edge: simplified o (n) planarity by edge addition. J Graph Algorithms Appl 8(2):241–273
Boyer JM, Myrvold WJ (2004b) On the cutting edge: simplified o(n) planarity by edge addition. J Graph Algorithms Appl 8(2):241–273. http://jgaa.info/accepted/2004/BoyerMyrvold2004.8.3.pdf
Brandenburg FJ (2014) 1-visibility representations of 1-planar graphs. J Graph Algorithms Appl 18(3):421–438. http://dx.doi.org/10.7155/jgaa.00330
Bruckdorfer T, Cornelsen S, Gutwenger C, Kaufmann M, Montecchiani F, Nöllenburg M, Wolff A (2012) Progress on partial edge drawings. In: Didimo W, Patrignani M (eds) Graph drawing - 20th international symposium, GD 2012, Redmond, September 19–21, 2012. Revised selected papers. Lecture notes in computer science, vol 7704. Springer, Berlin, pp 67–78. http://dx.doi.org/10.1007/978-3-642-36763-2_7
Buchheim C, Jünger M, Leipert S (2006) Drawing rooted trees in linear time. Softw Pract Exper 36(6):651–665. http://dx.doi.org/10.1002/spe.713
Burch M, Vehlow C, Konevtsova N, Weiskopf D (2012) Evaluating partially drawn links for directed graph edges. In: Graph drawing, Springer, Berlin, pp 226–237
Chimani M, Klein K (2013) Shrinking the search space for clustered planarity. In: Graph drawing, Springer, Berlin, pp 90–101
Chimani M, Gutwenger C, Jünger M, Klau GW, Klein K, Mutzel P (2013) The open graph drawing framework (OGDF). In: Tamassia R (ed) (2013) Handbook on graph drawing and visualization. Chapman and Hall/CRC, Boca Raton, pp 543–569. https://www.crcpress.com/Handbook-of-Graph-Drawing-and-Visualization/Tamassia/9781584884125
Chimani M, Di Battista G, Frati F, Klein K (2014) Advances on testing c-planarity of embedded flat clustered graphs. In: Graph drawing, Springer Berlin, Heidelberg, pp 416–427
Chrobak M, Eppstein D (1991) Planar orientations with low out-degree and compaction of adjacency matrices. Theor Comput Sci 86(2):243–266
Cortese PF, Di Battista G (2005) Clustered planarity. In: Proceedings of the twenty-first annual symposium on computational geometry. ACM, New York SCG ’05, pp 32–34. http://doi.acm.org/10.1145/1064092.1064093
Czauderna T, Klukas C, Schreiber F (2010) Editing, validating, and translating of SBGN maps. Bioinformatics 26(18):2340–2341
Dahlhaus E (1998) A linear time algorithm to recognize clustered graphs and its parallelization. In: Lucchesi CL, Moura AV (eds) LATIN ’98: theoretical Informatics. Third Latin American symposium, Campinas, April, 20–24, 1998, Proceedings. Lecture notes in computer science, vol 1380. Springer, Berlin, pp 239–248. http://dx.doi.org/10.1007/BFb0054325
Didimo W, Eades P, Liotta G (2009) Drawing graphs with right angle crossings. In: Dehne FKHA, Gavrilova ML, Sack J, Tóth CD (eds) Algorithms and data structures. 11th International Symposium, WADS 2009, Banff, August 21–23, 2009. Proceedings. Lecture notes in computer science, vol 5664, Springer, Berlin, pp 206–217. http://dx.doi.org/10.1007/978-3-642-03367-4_19
Dwyer T (2009) Scalable, versatile and simple constrained graph layout. Comput Graph Forum 28(3):991–998
Dwyer T, Mears C, Morgan K, Niven T, Marriott K, Wallace M (2014) Improved optimal and approximate power graph compression for clearer visualisation of dense graphs. In: Fujishiro I, Brandes U, Hagen H, Takahashi S (eds) IEEE pacific visualization symposium, PacificVis 2014, Yokohama, March 4–7, 2014. IEEE Computer Society, New York, pp 105–112. http://dx.doi.org/10.1109/PacificVis.2014.46
Eades P (1984) A heuristics for graph drawing. Congressus numerantium 42:146–160
Eades P, Liotta G (2013) Right angle crossing graphs and 1-planarity. Discrete Appl Math 161(7–8):961–969. http://dx.doi.org/10.1016/j.dam.2012.11.019
Eades P, Cohen RF, Huang ML (1997) Online animated graph drawing for web navigation. In: Battista GD (ed) (1997) Graph drawing. In: 5th international symposium, GD ’97, Rome, September 18–20, 1997, Proceedings. Lecture notes in computer science, vol 1353. Springer, Berlin, pp 330–335. http://dx.doi.org/10.1007/3-540-63938-1_77
Eades P, Feng Q, Nagamochi H (1999) Drawing clustered graphs on an orthogonal grid. J Graph Algorithms Appl 3(4):3–29. http://www.cs.brown.edu/publications/jgaa/accepted/99/EadesFengNagamochi99.3.4.pdf
Eades P, Hong S, Katoh N, Liotta G, Schweitzer P, Suzuki Y (2013) A linear time algorithm for testing maximal 1-planarity of graphs with a rotation system. Theor Comput Sci 513:65–76. http://dx.doi.org/10.1016/j.tcs.2013.09.029
Eades P, Hong S, Klein K, Nguyen A (2015) Shape-based quality metrics for large graph visualization. In: Giacomo ED, Lubiw A (eds) Graph drawing and network visualization - 23rd international symposium, GD 2015, Los Angeles, September 24–26, 2015. Revised selected papers. Lecture notes in computer science, vol 9411. Springer, Berlin, pp 502–514. http://dx.doi.org/10.1007/978-3-319-27261-0_41
Feng Q, Cohen RF, Eades P (1995) Planarity for clustered graphs. In: Spirakis PG (ed) Algorithms - ESA ’95, Third annual European symposium, Corfu, September 25–27, 1995, Proceedings. Lecture notes in computer science, Springer, Berlin, vol 979, pp 213–226. http://dx.doi.org/10.1007/3-540-60313-1_145
Fößmeier U, Kaufmann M (1995) Drawing high degree graphs with low bend numbers. In: Brandenburg F (ed) (1996) Graph drawing. In: Symposium on graph drawing, GD ’95, Passau, September 20–22, 1995, Proceedings. Lecture notes in computer science, vol 1027. Springer, Berlin, pp 254–266. http://dx.doi.org/10.1007/BFb0021809
Fruchterman TMJ, Reingold EM (1991) Graph drawing by force-directed placement. Softw Pract Exper 21(11):1129–1164. http://dx.doi.org/10.1002/spe.4380211102
Furnas GW (2006) A fisheye follow-up: further reflections on focus + context. In: Grinter RE, Rodden T, Aoki PM, Cutrell E, Jeffries R, Olson GM (eds) Proceedings of the 2006 conference on human factors in computing systems, CHI 2006, Montréal, Québec, April 22–27, 2006. ACM, New York, pp 999–1008. http://doi.acm.org/10.1145/1124772.1124921
Gajer P, Goodrich MT, Kobourov SG (2004) A multi-dimensional approach to force-directed layouts of large graphs. Comput Geom 29(1):3–18. http://dx.doi.org/10.1016/j.comgeo.2004.03.014
Gansner ER, Koutsofios E, North SC, Vo K (1993) A technique for drawing directed graphs. IEEE Trans Softw Eng 19(3):214–230. http://dx.doi.org/10.1109/32.221135
Gansner ER, Koren Y, North SC (2004) Graph drawing by stress majorization. In: Pach J (ed) (2004) Graph drawing. In: 12th international symposium, GD 2004, New York, September 29 - October 2, 2004. Revised selected papers. Lecture notes in computer science, vol 3383. Springer, Berlin, pp 239–250. http://dx.doi.org/10.1007/978-3-540-31843-9_25
Gansner ER, Hu Y, Kobourov SG (2010) Gmap: visualizing graphs and clusters as maps. In: IEEE pacific visualization symposium pacificVis 2010, Taipei, March 2–5, 2010. IEEE, New York, pp 201–208. http://dx.doi.org/10.1109/PACIFICVIS.2010.5429590
Gansner ER, Hu Y, Krishnan S (2013a) Coast: a convex optimization approach to stress-based embedding. In: Wismath SK, Wolff A (eds) Graph drawing. In: 21st international symposium, GD 2013, Bordeaux, September 23–25, 2013. Revised selected papers. Lecture notes in computer science, vol 8242. Springer, Berlin. http://dx.doi.org/10.1007/978-3-319-03841-4 pp 268–279. http://dx.doi.org/10.1007/978-3-319-03841-4
Gansner ER, Hu Y, North SC (2013b) A maxent-stress model for graph layout. IEEE Trans Vis Comput Graph 19(6):927–940. http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.299
Gansner ER, Hu Y, North SC (2013c) A maxent-stress model for graph layout. IEEE Trans Vis Comput Graph 19(6):927–940. http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.299
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman, New York
Garg A, Tamassia R (1996) A new minimum cost flow algorithm with applications to graph drawing. In: North SC (ed) Graph drawing, Symposium on graph drawing, GD ’96, Berkeley, September 18–20, Proceedings. Lecture notes in computer science, vol 1190. Springer, Berlin, pp 201–216. http://dx.doi.org/10.1007/3-540-62495-3_49
Ghoniem M, Fekete J, Castagliola P (2005) On the readability of graphs using node-link and matrix-based representations: a controlled experiment and statistical analysis. Inform Vis 4(2):114–135. http://dx.doi.org/10.1057/palgrave.ivs.9500092
Giacomo ED, Liotta G, Montecchiani F (2014) Drawing outer 1-planar graphs with few slopes. In: Duncan CA, Symvonis A (eds) Graph drawing - 22nd international symposium, GD 2014, Würzburg, September 24–26, 2014. Revised selected papers. Lecture notes in computer science, vol 8871. Springer, Berlin, pp 174–185. http://dx.doi.org/10.1007/978-3-662-45803-7_15
Gutwenger C, Jünger M, Leipert S, Mutzel P, Percan M, Weiskircher R (2002) Advances in c-planarity testing of clustered graphs. In: Goodrich M, Kobourov S (eds) Graph drawing. Lecture notes in computer science, vol 2528. Springer, Berlin, Heidelberg, pp 220–236. http://dx.doi.org/10.1007/3-540-36151-0_21
Gutwenger C, Jünger M, Klein K, Kupke J, Leipert S, Mutzel P (2003) A new approach for visualizing uml class diagrams. In: Proceedings of the 2003 ACM symposium on software visualization. ACM, New York, pp 179–188
Hachul S, Jünger M (2004) Drawing large graphs with a potential-field-based multilevel algorithm. In: Pach J (ed) (2004) Graph drawing. In: 12th international symposium, GD 2004, New York, September 29 - October 2, 2004. Revised selected papers. Lecture notes in computer science, vol 3383. Springer, Berlin, pp 285–295
Hachul S, Jünger M (2007) Large-graph layout algorithms at work: an experimental study. J Graph Algorithms Appl 11(2):345–369
Hadany R, Harel D (2001) A multi-scale algorithm for drawing graphs nicely. Discrete Applied Mathematics 113(1):3–21. http://dx.doi.org/10.1016/S0166-218X(00)00389-9
Hall K (1970) An r-dimensional quadratic placement algorithm. Management Science 17:219–229
Harel D, Koren Y (2002) A fast multi-scale method for drawing large graphs. J Graph Algorithms Appl 6(3):179–202, http://www.cs.brown.edu/publications/jgaa/accepted/2002/HarelKoren2002.6.3.pdf
Harel D, Koren Y (2004) Graph drawing by high-dimensional embedding. J Graph Algorithms Appl 8(2):195–214, http://jgaa.info/accepted/2004/HarelKoren2004.8.2.pdf
Holten D, van Wijk JJ (2009) Force-directed edge bundling for graph visualization. Comput Graph Forum 28(3):983–990. http://dx.doi.org/10.1111/j.1467-8659.2009.01450.x
Hopcroft JE, Tarjan RE (1974) Efficient planarity testing. J ACM 21(4):549–568. http://doi.acm.org/10.1145/321850.321852
Hu Y, Shi L (2015) Visualizing large graphs. Wiley Interdisciplinary Reviews: Computational Statistics 7(2):115–136. http://dx.doi.org/10.1002/wics.1343
Huang W, Eades P, Hong S (2014) Larger crossing angles make graphs easier to read. J Vis Lang Comput 25(4):452–465. http://dx.doi.org/10.1016/j.jvlc.2014.03.001
JelÃnková E, Kára J, KratochvÃl J, Pergel M, Suchý O, Vyskocil T (2009) Clustered planarity: Small clusters in cycles and Eulerian graphs. J Graph Algorithms Appl 13(3):379–422, http://jgaa.info/accepted/2009/Jelinkova+2009.13.3.pdf
Jia Y, Hoberock J, Garland M, Hart J (2008) On the visualization of social and other scale-free networks. IEEE Transactions on Visualization and Computer Graphics 14(6):1285–1292. https://doi.org/10.1109/TVCG.2008.151
Johnson B, Shneiderman B (1991) Tree maps: A space-filling approach to the visualization of hierarchical information structures. In: IEEE Visualization, pp 284–291. http://dx.doi.org/10.1109/VISUAL.1991.175815
Jünger M, Mutzel P (1994) The polyhedral approach to the maximum planar subgraph problem: New chances for related problems. In: Tamassia R, Tollis IG (eds) (1995) Graph drawing. In: DIMACS international workshop, GD ’94, Princeton, October 10–12, 1994, Proceedings. Lecture notes in computer science, vol 894. Springer, Berlin, pp 119–130. http://dx.doi.org/10.1007/3-540-58950-3_363
Jünger M, Mutzel P (1996) Maximum planar subgraphs and nice embeddings: Practical layout tools. Algorithmica 16(1):33–59. http://dx.doi.org/10.1007/BF02086607
Jünger M, Leipert S, Mutzel P (1998) A note on computing a maximal planar subgraph using pq-trees. IEEE Trans on CAD of Integrated Circuits and Systems 17(7):609–612. http://doi.ieeecomputersociety.org/10.1109/43.709399
Kamada T, Kawai S (1989) An algorithm for drawing general undirected graphs. Inf Process Lett 31(1):7–15. http://dx.doi.org/10.1016/0020-0190(89)90102-6
Karypis G, Kumar V (1995) Analysis of multilevel graph partitioning. In: Karin S (ed) Proceedings supercomputing ’95, San Diego, December 4-8, 1995. IEEE Computer Society/ACM, New York, p 29. http://doi.acm.org/10.1145/224170.224229
Khoury M, Hu Y, Krishnan S, Scheidegger CE (2012) Drawing large graphs by low-rank stress majorization. Comput Graph Forum 31(3):975–984. http://dx.doi.org/10.1111/j.1467-8659.2012.03090.x
Kobourov SG (2013) Force-directed drawing algorithms. Handbook of graph drawing and visualization, pp 383–408
Kobourov SG, Pupyrev S, Saket B (2014) Are crossings important for drawing large graphs? In: Graph drawing. Springer, Berlin, pp 234–245
Koren Y, Carmel L, Harel D (2002) ACE: a fast multiscale eigenvectors computation for drawing huge graphs. In: Wong PC, Andrews K (eds) 2002 IEEE symposium on information visualization (InfoVis 2002), 27 October–1 November 2002, Boston. IEEE Computer Society, New York, pp 137–144. http://dx.doi.org/10.1109/INFVIS.2002.1173159
Kuratowski K (1930) Sur le problème des courbes gauches en topologie. Fund Math 15:271–283
Lamping J, Rao R, Pirolli P (1995) A focus+context technique based on hyperbolic geometry for visualizing large hierarchies. In: Proceedings of the SIGCHI conference on human factors in computing systems, CHI ’95. ACM Press/Addison-Wesley, New York, pp 401–408. http://dx.doi.org/10.1145/223904.223956
Le Novère N, Hucka M, Mi H, Moodie S, Schreiber F, Sorokin A, Demir E, Wegner K, Aladjem M, Wimalaratne SM, Bergman FT, Gauges R, Ghazal P, Kawaji H, Li L, Matsuoka Y, Villéger A, Boyd SE, Calzone L, Courtot M, Dogrusoz U, Freeman T, Funahashi A, Ghosh S, Jouraku A, Kim S, Kolpakov F, Luna A, Sahle S, Schmidt E, Watterson S, Wu G, Goryanin I, Kell DB, Sander C, Sauro H, Snoep JL, Kohn K, Kitano H (2009) The systems biology graphical notation. Nat Biotechnol 27:735–741
Lin T, Eades P (1994) Integration of declarative and algorithmic approaches for layout creation. In: Tamassia R, Tollis IG (eds) (1995) Graph drawing. In: DIMACS international workshop, GD ’94, Princeton, October 10–12, 1994, Proceedings. Lecture notes in computer science, vol 894. Springer, Berlin, pp 376–387. http://dx.doi.org/10.1007/3-540-58950-3_392
Mehlhorn K, Mutzel P (1996) On the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. Algorithmica 16(2):233–242. http://dx.doi.org/10.1007/BF01940648
Misue K, Eades P, Lai W, Sugiyama K (1995) Layout adjustment and the mental map. J Vis Lang Comput 6(2):183–210. http://dx.doi.org/10.1006/jvlc.1995.1010
Monash University (2015) WebCoLa – constraint-based layout in the browser. http://marvl.infotech.monash.edu/webcola/
Newbery FJ (1989) Edge concentration: a method for clustering directed graphs. In: SCM, pp 76–85
Nguyen QH, Eades P, Hong S (2013) On the faithfulness of graph visualizations. In: Carpendale S, Chen W, Hong S (eds) IEEE pacific visualization symposium, PacificVis 2013, February 27 2013-March 1, 2013, Sydney. IEEE, New York, pp 209–216. http://dx.doi.org/10.1109/PacificVis.2013.6596147
Nocaj A, Ortmann M, Brandes U (2016) Adaptive disentanglement based on local clustering in small-world network visualization. IEEE Trans Vis Comput Graph. http://dx.doi.org/10.1109/TVCG.2016.2534559
OGDF (2015) The open graph drawing framework. http://www.ogdf.net
Purchase HC (2002) Metrics for graph drawing aesthetics. J Vis Lang Comput 13(5):501–516. http://dx.doi.org/10.1006/jvlc.2002.0232
Purchase HC, Cohen RF, James MI (1995) Validating graph drawing aesthetics. In: Brandenburg F (ed) (1996) Graph drawing. In: Symposium on graph drawing, GD ’95, Passau, September 20–22, 1995, Proceedings. Lecture notes in computer science, vol 1027. Springer, Berlin, pp 435–446. http://dx.doi.org/10.1007/BFb0021827
Quigley A, Eades P (2001) Fade: graph drawing, clustering, and visual abstraction. In: Graph drawing. Springer, Berlin, Heidelberg, pp 197–210
Reingold EM, Tilford JS (1981) Tidier drawings of trees. IEEE Trans Softw Eng 7(2):223–228. http://dx.doi.org/10.1109/TSE.1981.234519
Rohn H, Junker A, Hartmann A, Grafahrend-Belau E, Treutler H, Klapperstuck M, Czauderna T, Klukas C, Schreiber F (2012) Vanted v2: a framework for systems biology applications. BMC Syst Biol 6:139
Rüegg U, Kieffer S, Dwyer T, Marriott K, Wybrow M (2014) Stress-minimizing orthogonal layout of data flow diagrams with ports. In: Graph drawing. Springer, Berlin, pp 319–330
Rusu A (2013) Three drawing algorithms. In: Tamassia R (ed) (2013) Handbook on graph drawing and visualization. Chapman and Hall/CRC, Boca Raton, pp 155–192. https://www.crcpress.com/Handbook-of-Graph-Drawing-and-Visualization/Tamassia/9781584884125
Schreiber F, Dwyer T, Marriott K, Wybrow M (2009) A generic algorithm for layout of biological networks. BMC Bioinform 10:375
Shih W, Hsu W (1999) A new planarity test. Theor Comput Sci 223(1–2):179–191. http://dx.doi.org/10.1016/S0304-3975(98)00120-0
Sugiyama K, Tagawa S, Toda M (1981) Methods for visual understanding of hierarchical system structures. IEEE Trans Syst Man Cybern 11(2):109–125. http://dx.doi.org/10.1109/TSMC.1981.4308636
Sultana S, Rahman MS, Roy A, Tairin S (2014) Bar 1-visibility drawings of 1-planar graphs. In: Gupta P, Zaroliagis CD (eds) Applied algorithms - first international conference, ICAA 2014, Kolkata, January 13–15, 2014. Proceedings. Lecture notes in computer science, vol 8321. Springer, Berlin, pp 62–76. http://dx.doi.org/10.1007/978-3-319-04126-1_6
Tamassia R (1987) On embedding a graph in the grid with the minimum number of bends. SIAM J Comput 16(3):421–444. http://dx.doi.org/10.1137/0216030
Tamassia R, Tollis IG (1986) Algorithms for visibility representations of planar graphs. In: Monien B, Vidal-Naquet G (eds) STACS 86, 3rd annual symposium on theoretical aspects of computer science, Orsay, January 16–18, 1986, Proceedings. Lecture notes in computer science, vol 210. Springer, Berlin, pp 130–141. http://dx.doi.org/10.1007/3-540-16078-7_71
Tamassia R, Battista GD, Batini C (1988) Automatic graph drawing and readability of diagrams. IEEE Trans Syst Man Cybern 18(1):61–79. http://dx.doi.org/10.1109/21.87055
Tom Sawyer Software (2015) Tom sawyer toolkit. https://www.tomsawyer.com/
Torgerson WS (1952) Multidimensional scaling: I. theory and method. Psychometrika 17(4):401–419. http://dx.doi.org/10.1007/BF02288916
Tufte ER (1992) The visual display of quantitative information. Graphics Press, Cheshire
TULIP (2015) The Tulip framework. tulip.labri.fr
Tutte WT (1960) Convex representations of graphs. Proc Lond Math Soc 10:304–320
Tutte WT (1963) How to draw a graph. Proc Lond Math Soc 13:743–767
University of Florida (2015) The university of Florida sparse matrix collection. http://www.cise.ufl.edu/research/sparse/matrices/
Walshaw C (2003) A multilevel algorithm for force-directed graph-drawing. J Graph Algorithms Appl 7(3):253–285. http://www.cs.brown.edu/publications/jgaa/accepted/2003/Walshaw2003.7.3.pdf
Ware C, Purchase HC, Colpoys L, McGill M (2002) Cognitive measurements of graph aesthetics. Inf. Vis. 1(2):103–110. http://dx.doi.org/10.1057/palgrave.ivs.9500013
Yoghourdjian V, Dwyer T, Gange G, Kieffer S, Klein K, Marriott K (2016) High-quality ultra-compact grid layout of grouped networks. IEEE Trans Vis Comput Graph 22(1):339–348. http://doi.ieeecomputersociety.org/10.1109/TVCG.2015.2467251
Yunis E, Yokota R, Ahmadia AJ (2012) Scalable force directed graph layout algorithms using fast multipole methods. In: Bader M, Bungartz H, Grigoras D, Mehl M, Mundani R, Potolea R (eds) 11th international symposium on parallel and distributed computing, ISPDC 2012, Munich, June 25–29, 2012. IEEE Computer Society, New York, pp 180–187. http://dx.doi.org/10.1109/ISPDC.2012.32
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Eades, P., Klein, K. (2018). Graph Visualization. In: Fletcher, G., Hidders, J., Larriba-Pey, J. (eds) Graph Data Management. Data-Centric Systems and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-96193-4_2
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