Visualization of node-link graphs Graphic representation of a minute fraction of the WWW, demonstrating hyperlinks. Symmetry display is the problem of finding symmetry groups within a given graph, and finding a drawing that displays as much of the symmetry as possible. Some layout methods automatically lead to symmetric drawings; alternatively, some drawing methods start by finding symmetries in the input graph and using them to construct a drawing. [11] Kaufmann, Michael; Wagner, Dorothea, eds. (2001), Drawing Graphs: Methods and Models, Lecture Notes in Computer Science, vol.2025, Springer-Verlag, doi: 10.1007/3-540-44969-8, ISBN 978-3-540-42062-0, S2CID 1808286 . Several commonly used quality measures concern lengths of edges: it is generally desirable to minimize the total length of the edges as well as the maximum length of any edge. Additionally, it may be preferable for the lengths of edges to be uniform rather than highly varied.

Di Battista et al. (1994), Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; ( Eiglsperger, Fekete & Klau 2001). Misue, K.; Eades, P.; Lai, W.; Sugiyama, K. (1995), "Layout Adjustment and the Mental Map", Journal of Visual Languages & Computing, 6 (2): 183–210, doi: 10.1006/jvlc.1995.1010 . Many different quality measures have been defined for graph drawings, in an attempt to find objective means of evaluating their aesthetics and usability. [9] In addition to guiding the choice between different layout methods for the same graph, some layout methods attempt to directly optimize these measures. BioFabric open-source software for visualizing large networks by drawing nodes as horizontal lines. Graphviz and Dynagraph – Static and Dynamic Graph Drawing Tools", by John Ellson, Emden R. Gansner, Eleftherios Koutsofios, Stephen C. North, and Gordon Woodhull, in Jünger & Mutzel (2004).

Draw on graph paper online

Orthogonal layout methods, which allow the edges of the graph to run horizontally or vertically, parallel to the coordinate axes of the layout. These methods were originally designed for VLSI and PCB layout problems but they have also been adapted for graph drawing. They typically involve a multiphase approach in which an input graph is planarized by replacing crossing points by vertices, a topological embedding of the planarized graph is found, edge orientations are chosen to minimize bends, vertices are placed consistently with these orientations, and finally a layout compaction stage reduces the area of the drawing. [16] Tamassia, Roberto, ed. (2014), Handbook of Graph Drawing and Visualization, CRC Press, archived from the original on 2013-08-15 , retrieved 2013-08-28 .

Freese, Ralph (2004), "Automated lattice drawing", in Eklund, Peter (ed.), Concept Lattices: Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23-26, 2004, Proceedings (PDF), Lecture Notes in Computer Science, vol.2961, Springer-Verlag, pp.589–590, CiteSeerX 10.1.1.69.6245, doi: 10.1007/978-3-540-24651-0_12, ISBN 978-3-540-21043-6, archived (PDF) from the original on 2016-03-14 , retrieved 2011-09-17 .Eiglsperger, Markus; Fekete, Sándor; Klau, Gunnar (2001), "Orthogonal graph drawing", in Kaufmann, Michael; Wagner, Dorothea (eds.), Drawing Graphs, Lecture Notes in Computer Science, vol.2025, Springer Berlin / Heidelberg, pp.121–171, doi: 10.1007/3-540-44969-8_6, ISBN 978-3-540-42062-0 . Di Battista, Giuseppe; Eades, Peter; Tamassia, Roberto; Tollis, Ioannis G. (1998), Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall, ISBN 978-0-13-301615-4 .

Di Battista et al. (1994), pp. 15–16, and Chapter 6, "Flow and Upward Planarity", pp. 171–214; Freese (2004). Mathematica, a general purpose computation tool that includes 2D and 3D graph visualization and graph analysis tools. [29] [30] Bastert, Oliver; Matuszewski, Christian (2001), "Layered drawings of digraphs", in Kaufmann, Michael; Wagner, Dorothea (eds.), Drawing Graphs: Methods and Models, Lecture Notes in Computer Science, vol.2025, Springer-Verlag, pp.87–120, doi: 10.1007/3-540-44969-8_5, ISBN 978-3-540-42062-0 . Sociograms, drawings of a social network, as often offered by social network analysis software [22] Scott, John (2000), "Sociograms and Graph Theory", Social network analysis: a handbook (2nded.), Sage, pp.64–69, ISBN 978-0-7619-6339-4 .Longabaugh, William (2012), "Combing the hairball with BioFabric: a new approach for visualization of large networks", BMC Bioinformatics, 13: 275, doi: 10.1186/1471-2105-13-275, PMC 3574047, PMID 23102059 {{ citation}}: CS1 maint: unflagged free DOI ( link). Brandes, Ulrik; Freeman, Linton C.; Wagner, Dorothea (2014), "Social Networks", in Tamassia, Roberto (ed.), Handbook of Graph Drawing and Visualization, CRC Press, pp.805–839 . Angular resolution is a measure of the sharpest angles in a graph drawing. If a graph has vertices with high degree then it necessarily will have small angular resolution, but the angular resolution can be bounded below by a function of the degree. [12] Jünger, Michael; Mutzel, Petra (2004), Graph Drawing Software, Springer-Verlag, ISBN 978-3-540-00881-1 . Spectral layout methods use as coordinates the eigenvectors of a matrix such as the Laplacian derived from the adjacency matrix of the graph. [15]

The crossing number of a drawing is the number of pairs of edges that cross each other. If the graph is planar, then it is often convenient to draw it without any edge intersections; that is, in this case, a graph drawing represents a graph embedding. However, nonplanar graphs frequently arise in applications, so graph drawing algorithms must generally allow for edge crossings. [10]Anderson, James Andrew; Head, Thomas J. (2006), Automata Theory with Modern Applications, Cambridge University Press, pp.38–41, ISBN 978-0-521-84887-9 . Bachmaier, Christian; Brandes, Ulrik; Schreiber, Falk (2014), "Biological Networks", in Tamassia, Roberto (ed.), Handbook of Graph Drawing and Visualization, CRC Press, pp.621–651 . The slope number of a graph is the minimum number of distinct edge slopes needed in a drawing with straight line segment edges (allowing crossings). Cubic graphs have slope number at most four, but graphs of degree five may have unbounded slope number; it remains open whether the slope number of degree-4 graphs is bounded. [12] Pach, János; Sharir, Micha (2009), "5.5 Angular resolution and slopes", Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, vol.152, American Mathematical Society, pp.126–127 .