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Graph drawing
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==Graphical conventions== [[File:4node-digraph-natural.svg|thumb|upright=0.5|[[Directed graph]] with arrowheads showing edge directions]] Graphs are frequently drawn as node–link diagrams in which the vertices are represented as disks, boxes, or textual labels and the edges are represented as [[line segment]]s, [[Polygonal chain|polylines]], or curves in the [[Euclidean plane]].<ref name="dett-viii">{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1998}}, p. viii.</ref> 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 graph]]s in order to analyze all pairwise combinations among sets of metaphysical concepts.{{sfnp|Knuth|2013}} In the case of [[directed graph]]s, [[Arrow (symbol)|arrowheads]] form a commonly used graphical convention to show their [[Orientability|orientation]];<ref name="dett6"/> however, user studies have shown that other conventions such as tapering provide this information more effectively.<ref>{{harvtxt|Holten|van Wijk|2009}}; {{harvtxt|Holten|Isenberg|van Wijk|Fekete|2011}}.</ref> [[Upward planar drawing]] uses the convention that every edge is oriented from a lower vertex to a higher vertex, making arrowheads unnecessary.{{sfnp|Garg|Tamassia|1995}} Alternative conventions to node–link diagrams include adjacency representations such as [[circle packing theorem|circle packings]], in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies between regions; [[intersection graph|intersection representations]] in which vertices are represented by 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 [[train track (mathematics)|train tracks]]; fabrics, in which nodes are represented as horizontal lines and edges as vertical lines;<ref name="Longabaugh 2012">{{harvtxt|Longabaugh|2012}}.</ref> and visualizations of the [[adjacency matrix]] of the graph.
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