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Draw a Circle Around Nodes Graphviz Python

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Visualization of node-link graphs

Graphic representation of a minute fraction of the WWW, demonstrating hyperlinks.

Graph drawing is an area of mathematics and information science combining methods from geometric graph theory and information visualization to derive 2-dimensional depictions of graphs arising from applications such equally social network analysis, cartography, linguistics, and bioinformatics.[i]

A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not exist confused with the graph itself: very different layouts tin can correspond to the same graph.[2] In the abstruse, all that matters is which pairs of vertices are connected by edges. In the concrete, however, the system of these vertices and edges within a drawing affects its understandability, usability, fabrication price, and aesthetics.[3] The problem gets worse if the graph changes over time by adding and deleting edges (dynamic graph drawing) and the goal is to preserve the user's mental map.[4]

Graphical conventions [edit]

Graphs are often fatigued every bit node–link diagrams in which the vertices are represented as disks, boxes, or textual labels and the edges are represented as line segments, polylines, or curves in the Euclidean plane.[iii] Node–link diagrams can be traced back to the 14th-16th century works of Pseudo-Lull which were published under the name of Ramon Llull, a 13th century polymath. Pseudo-Lull drew diagrams of this type for complete graphs in society to clarify all pairwise combinations among sets of metaphysical concepts.[five]

In the case of directed graphs, arrowheads form a commonly used graphical convention to prove their orientation;[2] however, user studies accept shown that other conventions such as tapering provide this information more finer.[6] Upward planar cartoon uses the convention that every edge is oriented from a lower vertex to a higher vertex, making arrowheads unnecessary.[vii]

Alternative conventions to node–link diagrams include adjacency representations such as circumvolve packings, in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies betwixt regions; intersection representations in which vertices are represented past non-disjoint geometric objects and edges are represented by their intersections; visibility representations in which vertices are represented by regions in the plane and edges are represented by regions that have an unobstructed line of sight to each other; confluent drawings, in which edges are represented as smooth curves within mathematical railroad train tracks; fabrics, in which nodes are represented equally horizontal lines and edges equally vertical lines;[8] and visualizations of the adjacency matrix of the graph.

Quality measures [edit]

Many different quality measures have been divers for graph drawings, in an attempt to find objective means of evaluating their aesthetics and usability.[9] In addition to guiding the choice betwixt dissimilar layout methods for the aforementioned graph, some layout methods attempt to directly optimize these measures.

  • The crossing number of a drawing is the number of pairs of edges that cross each other. If the graph is planar, and then it is often convenient to depict information technology without whatsoever border 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 more often than not permit for border crossings.[10]
  • The surface area of a drawing is the size of its smallest bounding box, relative to the closest distance between whatsoever 2 vertices. Drawings with smaller area are generally preferable to those with larger area, because they permit the features of the cartoon to be shown at greater size and therefore more legibly. The attribute ratio of the bounding box may also be important.
  • Symmetry display is the problem of finding symmetry groups within a given graph, and finding a drawing that displays equally much of the symmetry as possible. Some layout methods automatically lead to symmetric drawings; alternatively, some cartoon methods start by finding symmetries in the input graph and using them to construct a cartoon.[eleven]
  • It is important that edges accept shapes that are as simple as possible, to make it easier for the centre to follow them. In polyline drawings, the complexity of an border may be measured by its number of bends, and many methods aim to provide drawings with few total bends or few bends per edge. Similarly for spline curves the complication of an edge may be measured past the number of control points on the border.
  • Several commonly used quality measures business concern lengths of edges: it is generally desirable to minimize the total length of the edges as well as the maximum length of whatsoever edge. Additionally, information technology may be preferable for the lengths of edges to be uniform rather than highly varied.
  • Angular resolution is a measure of the sharpest angles in a graph drawing. If a graph has vertices with high degree then information technology necessarily will have small angular resolution, just the angular resolution can be bounded beneath by a function of the degree.[12]
  • The gradient number of a graph is the minimum number of distinct edge slopes needed in a drawing with straight line segment edges (assuasive crossings). Cubic graphs take gradient number at most 4, but graphs of degree five may have unbounded slope number; it remains open whether the gradient number of caste-iv graphs is bounded.[12]

Layout methods [edit]

A force-based network visualization.[13]

At that place are many unlike graph layout strategies:

  • In forcefulness-based layout systems, the graph drawing software modifies an initial vertex placement by continuously moving the vertices according to a system of forces based on physical metaphors related to systems of springs or molecular mechanics. Typically, these systems combine bonny forces between next vertices with repulsive forces between all pairs of vertices, in society to seek a layout in which border lengths are pocket-sized while vertices are well-separated. These systems may perform gradient descent based minimization of an free energy office, or they may translate the forces directly into velocities or accelerations for the moving vertices.[14]
  • Spectral layout methods use as coordinates the eigenvectors of a matrix such as the Laplacian derived from the adjacency matrix of the graph.[15]
  • Orthogonal layout methods, which let 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 likewise been adapted for graph drawing. They typically involve a multiphase approach in which an input graph is planarized past replacing crossing points by vertices, a topological embedding of the planarized graph is institute, border orientations are chosen to minimize bends, vertices are placed consistently with these orientations, and finally a layout compaction stage reduces the area of the cartoon.[sixteen]
  • Tree layout algorithms these show a rooted tree-similar formation, suitable for trees. Often, in a technique called "airship layout", the children of each node in the tree are drawn on a circle surrounding the node, with the radii of these circles diminishing at lower levels in the tree so that these circles do not overlap.[17]
  • Layered graph drawing methods (frequently called Sugiyama-style drawing) are best suited for directed acyclic graphs or graphs that are nearly acyclic, such as the graphs of dependencies between modules or functions in a software organisation. In these methods, the nodes of the graph are arranged into horizontal layers using methods such as the Coffman–Graham algorithm, in such a way that nigh edges go downwards from one layer to the adjacent; after this step, the nodes within each layer are arranged in order to minimize crossings.[xviii]

  • Arc diagrams, a layout style dating back to the 1960s,[19] place vertices on a line; edges may exist drawn as semicircles higher up or beneath the line, or as smooth curves linked together from multiple semicircles.
  • Circular layout methods place the vertices of the graph on a circle, choosing carefully the ordering of the vertices effectually the circle to reduce crossings and place adjacent vertices close to each other. Edges may be drawn either as chords of the circumvolve or as arcs inside or outside of the circumvolve. In some cases, multiple circles may be used.[20]
  • Authorization drawing places vertices in such a mode that one vertex is upward, rightwards, or both of another if and but if information technology is reachable from the other vertex. In this way, the layout manner makes the reachability relation of the graph visually apparent.[21]

Application-specific graph drawings [edit]

Graphs and graph drawings arising in other areas of awarding include

  • Sociograms, drawings of a social network, as often offered past social network assay software[22]
  • Hasse diagrams, a type of graph drawing specialized to partial orders[23]
  • Dessin d'enfants, a blazon of graph cartoon used in algebraic geometry[24]
  • State diagrams, graphical representations of finite-state machines[25]
  • Reckoner network diagrams, depictions of the nodes and connections in a reckoner network[26]
  • Flowcharts and drakon-charts, drawings in which the nodes represent the steps of an algorithm and the edges represent control menstruum between steps.
  • Data-flow diagrams, drawings in which the nodes correspond the components of an information system and the edges represent the move of information from i component to some other.
  • Bioinformatics including phylogenetic trees, protein–poly peptide interaction networks, and metabolic pathways.[27]

In addition, the placement and routing steps of electronic design automation (EDA) are similar in many means to graph cartoon, as is the problem of greedy embedding in distributed computing, and the graph drawing literature includes several results borrowed from the EDA literature. Notwithstanding, these problems also differ in several of import ways: for instance, in EDA, area minimization and signal length are more important than aesthetics, and the routing problem in EDA may have more than two terminals per internet while the analogous problem in graph drawing generally only involves pairs of vertices for each edge.

Software [edit]

A graph drawing interface (Gephi 0.nine.1)

Software, systems, and providers of systems for drawing graphs include:

  • BioFabric open-source software for visualizing big networks by drawing nodes as horizontal lines.
  • Cytoscape, open up-source software for visualizing molecular interaction networks
  • Gephi, open up-source network assay and visualization software
  • graph-tool, a complimentary/libre Python library for analysis of graphs.
  • Graphviz, an open-source graph cartoon system from AT&T Corporation[28]
  • Linkurious, a commercial network analysis and visualization software for graph databases
  • Mathematica, a general purpose computation tool that includes 2d and 3D graph visualization and graph analysis tools.[29] [thirty]
  • Microsoft Automatic Graph Layout, open-source .NET library (formerly chosen GLEE) for laying out graphs[31]
  • NetworkX is a Python library for studying graphs and networks.
  • Tulip (software),[32] an open source information visualization tool
  • yEd, a graph editor with graph layout functionality[33]
  • PGF/TikZ 3.0 with the graphdrawing package (requires LuaTeX).[34]
  • LaNet-vi, an open-source large network visualization software
  • Edraw Max 2nd business technical diagramming software

References [edit]

Footnotes
  1. ^ Di Battista et al. (1994), pp. vii–8; Herman, Melançon & Marshall (2000), Section i.one, "Typical Application Areas".
  2. ^ a b Di Battista et al. (1994), p. 6.
  3. ^ a b Di Battista et al. (1994), p. viii.
  4. ^ Misue et al. (1995)
  5. ^ Knuth, Donald E. (2013), "Two grand years of combinatorics", in Wilson, Robin; Watkins, John J. (eds.), Combinatorics: Ancient and Modern, Oxford University Printing, pp. seven–37 .
  6. ^ Holten & van Wijk (2009); Holten et al. (2011).
  7. ^ Garg & Tamassia (1995).
  8. ^ Longabaugh (2012).
  9. ^ Di Battista et al. (1994), Section 2.1.2, Aesthetics, pp. 14–16; Purchase, Cohen & James (1997).
  10. ^ Di Battista et al. (1994), p 14.
  11. ^ Di Battista et al. (1994), p. 16.
  12. ^ a b Pach & Sharir (2009).
  13. ^ Published in Grandjean, Martin (2014). "La connaissance est un réseau". Les Cahiers du Numérique. 10 (3): 37–54. doi:10.3166/lcn.10.3.37-54. Retrieved 2014-x-15 .
  14. ^ Di Battista et al. (1994), Section 2.7, "The Force-Directed Approach", pp. 29–30, and Affiliate 10, "Forcefulness-Directed Methods", pp. 303–326.
  15. ^ Beckman (1994); Koren (2005).
  16. ^ Di Battista et al. (1994), Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; (Eiglsperger, Fekete & Klau 2001).
  17. ^ Herman, Melançon & Marshall (2000), Section 2.2, "Traditional Layout – An Overview".
  18. ^ Sugiyama, Tagawa & Toda (1981); Bastert & Matuszewski (2001); Di Battista et al. (1994), Chapter 9, "Layered Drawings of Digraphs", pp. 265–302.
  19. ^ Saaty (1964).
  20. ^ Doğrusöz, Madden & Madden (1997).
  21. ^ Di Battista et al. (1994), Department 4.7, "Authority Drawings", pp. 112–127.
  22. ^ Scott (2000); Brandes, Freeman & Wagner (2014).
  23. ^ Di Battista et al. (1994), pp. 15–sixteen, and Chapter 6, "Flow and Upwardly Planarity", pp. 171–214; Freese (2004).
  24. ^ Zapponi (2003).
  25. ^ Anderson & Caput (2006).
  26. ^ Di Battista & Rimondini (2014).
  27. ^ Bachmaier, Brandes & Schreiber (2014).
  28. ^ "Graphviz and Dynagraph – Static and Dynamic Graph Drawing Tools", by John Ellson, Emden R. Gansner, Eleftherios Koutsofios, Stephen C. N, and Gordon Woodhull, in Jünger & Mutzel (2004).
  29. ^ GraphPlot Mathematica documentation
  30. ^ Graph drawing tutorial
  31. ^ Nachmanson, Robertson & Lee (2008).
  32. ^ "Tulip – A Huge Graph Visualization Framework", by David Auber, in Jünger & Mutzel (2004).
  33. ^ "yFiles – Visualization and Automatic Layout of Graphs", by Roland Wiese, Markus Eiglsperger, and Michael Kaufmann, in Jünger & Mutzel (2004).
  34. ^ Tantau (2013); see as well the older GD 2012 presentation
General references
  • Di Battista, Giuseppe; Eades, Peter; Tamassia, Roberto; Tollis, Ioannis G. (1994), "Algorithms for Drawing Graphs: an Annotated Bibliography", Computational Geometry: Theory and Applications, 4 (five): 235–282, doi:10.1016/0925-7721(94)00014-x .
  • Di Battista, Giuseppe; Eades, Peter; Tamassia, Roberto; Tollis, Ioannis M. (1998), Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall, ISBN978-0-13-301615-4 .
  • Herman, Ivan; Melançon, Guy; Marshall, M. Scott (2000), "Graph Visualization and Navigation in Information Visualization: A Survey", IEEE Transactions on Visualization and Figurer Graphics, 6 (1): 24–43, doi:10.1109/2945.841119 .
  • Jünger, Michael; Mutzel, Petra (2004), Graph Cartoon Software, Springer-Verlag, ISBN978-3-540-00881-one .
  • Kaufmann, Michael; Wagner, Dorothea, eds. (2001), Drawing Graphs: Methods and Models, Lecture Notes in Calculator Scientific discipline, vol. 2025, Springer-Verlag, doi:10.1007/3-540-44969-8, ISBN978-3-540-42062-0, S2CID 1808286 .
  • Tamassia, Roberto, ed. (2014), Handbook of Graph Drawing and Visualization, CRC Printing, archived from the original on 2013-08-fifteen, retrieved 2013-08-28 .
Specialized subtopics
  • Anderson, James Andrew; Head, Thomas J. (2006), Automata Theory with Modern Applications, Cambridge University Press, pp. 38–41, ISBN978-0-521-84887-ix .
  • Bachmaier, Christian; Brandes, Ulrik; Schreiber, Falk (2014), "Biological Networks", in Tamassia, Roberto (ed.), Handbook of Graph Cartoon and Visualization, CRC Press, pp. 621–651 .
  • 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/three-540-44969-8_5, ISBN978-three-540-42062-0 .
  • Beckman, Brian (1994), Theory of Spectral Graph Layout, Tech. Report MSR-TR-94-04, Microsoft Research .
  • 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 .
  • Di Battista, Giuseppe; Rimondini, Massimo (2014), "Estimator Networks", in Tamassia, Roberto (ed.), Handbook of Graph Drawing and Visualization, CRC Press, pp. 763–803 .
  • Doğrusöz, Uğur; Madden, Brendan; Madden, Patrick (1997), "Circular layout in the Graph Layout toolkit", in North, Stephen (ed.), Symposium on Graph Drawing, GD '96 Berkeley, California, United states of america, September eighteen–20, 1996, Proceedings, Lecture Notes in Reckoner Scientific discipline, vol. 1190, Springer-Verlag, pp. 92–100, doi:ten.1007/iii-540-62495-3_40, ISBN978-3-540-62495-0 .
  • 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, ISBN978-3-540-42062-0 .
  • Freese, Ralph (2004), "Automated lattice drawing", in Eklund, Peter (ed.), Concept Lattices: 2nd International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, Feb 23-26, 2004, Proceedings (PDF), Lecture Notes in Reckoner Science, vol. 2961, Springer-Verlag, pp. 589–590, CiteSeerXten.1.1.69.6245, doi:10.1007/978-3-540-24651-0_12, ISBN978-iii-540-21043-vi .
  • Garg, Ashim; Tamassia, Roberto (1995), "Upward planarity testing", Guild, 12 (2): 109–133, CiteSeerXten.1.ane.x.2237, doi:10.1007/BF01108622, MR 1354797, S2CID 14183717 .
  • Holten, Danny; Isenberg, Petra; van Wijk, Jarke J.; Fekete, Jean-Daniel (2011), "An extended evaluation of the readability of tapered, animated, and textured directed-border representations in node-link graphs", IEEE Pacific Visualization Symposium (PacificVis 2011) (PDF), pp. 195–202, doi:10.1109/PACIFICVIS.2011.5742390, ISBN978-1-61284-935-5, S2CID 16526781 .
  • Holten, Danny; van Wijk, Jarke J. (2009), "A user written report on visualizing directed edges in graphs", Proceedings of the 27th International Conference on Human Factors in Computing Systems (CHI '09) (PDF), pp. 2299–2308, CiteSeerXx.one.1.212.5461, doi:10.1145/1518701.1519054, ISBN9781605582467, S2CID 9725345, archived from the original (PDF) on 2011-11-06 .
  • Koren, Yehuda (2005), "Drawing graphs by eigenvectors: theory and practice", Computers & Mathematics with Applications, 49 (11–12): 1867–1888, doi:10.1016/j.camwa.2004.08.015, MR 2154691 .
  • 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, PMC3574047, PMID 23102059 .
  • Madden, Brendan; Madden, Patrick; Powers, Steve; Himsolt, Michael (1996), "Portable graph layout and editing", in Brandenburg, Franz J. (ed.), Graph Drawing: Symposium on Graph Drawing, GD '95, Passau, Federal republic of germany, September 20–22, 1995, Proceedings, Lecture Notes in Computer Science, vol. 1027, Springer-Verlag, pp. 385–395, doi:ten.1007/BFb0021822, ISBN978-3-540-60723-6 .
  • Misue, K.; Eades, P.; Lai, Due west.; Sugiyama, M. (1995), "Layout Adjustment and the Mental Map", Journal of Visual Languages & Computing, 6 (2): 183–210, doi:10.1006/jvlc.1995.1010 .
  • Nachmanson, Lev; Robertson, George; Lee, Bongshin (2008), "Cartoon Graphs with GLEE" (PDF), in Hong, Seok-Hee; Nishizeki, Takao; Quan, Wu (eds.), Graph Cartoon, 15th International Symposium, GD 2007, Sydney, Commonwealth of australia, September 24–26, 2007, Revised Papers, Lecture Notes in Estimator Science, vol. 4875, Springer-Verlag, pp. 389–394, doi:ten.1007/978-three-540-77537-9_38, ISBN978-3-540-77536-2 .
  • 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 Order, pp. 126–127 .
  • Purchase, H. C.; Cohen, R. F.; James, M. I. (1997), "An experimental study of the basis for graph drawing algorithms" (PDF), Journal of Experimental Algorithmics, 2, Article four, doi:10.1145/264216.264222, S2CID 22076200 [ permanent expressionless link ] .
  • Saaty, Thomas L. (1964), "The minimum number of intersections in complete graphs", Proc. Natl. Acad. Sci. U.S.A., 52 (iii): 688–690, Bibcode:1964PNAS...52..688S, doi:10.1073/pnas.52.3.688, PMC300329, PMID 16591215 .
  • Scott, John (2000), "Sociograms and Graph Theory", Social network assay: a handbook (2nd ed.), Sage, pp. 64–69, ISBN978-0-7619-6339-4 .
  • Sugiyama, Kozo; Tagawa, Shôjirô; Toda, Mitsuhiko (1981), "Methods for visual understanding of hierarchical system structures", IEEE Transactions on Systems, Homo, and Cybernetics, SMC-11 (2): 109–125, doi:10.1109/TSMC.1981.4308636, MR 0611436, S2CID 8367756 .
  • Tantau, Till (2013), "Graph Drawing in TikZ", Journal of Graph Algorithms and Applications, 17 (4): 495–513, doi:x.7155/jgaa.00301 .
  • Zapponi, Leonardo (August 2003), "What is a Dessin d'Enfant" (PDF), Notices of the American Mathematical Society, 50: 788–789 .

External links [edit]

  • GraphX library for .Internet: open up-source WPF library for graph calculation and visualization. Supports many layout and edge routing algorithms.
  • Graph drawing e-impress annal: including data on papers from all Graph Cartoon symposia.
  • Graph drawing at Curlie for many additional links related to graph drawing.

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Source: https://en.wikipedia.org/wiki/Graph_drawing

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