View source for Radial tree

{{Short description|Mathematical tree on concentric circles}}
[[File:Radial tree - Graphic Statistics in Management.svg|thumb|right|upright=1.35|Example of a radial tree, from a 1924 organization chart that emphasizes a central authority<ref>W. H. Smith., Graphic Statistics in Management (McGraw-Hill Book Company, New York, ed. First, 1924) http://www.visualcomplexity.com/vc/project.cfm?id=10</ref>]] 
A '''radial tree''', or '''radial map''', is a method of displaying a [[tree structure]] (e.g., a [[Tree (data structure)|tree data structure]]) in a way that expands outwards, radially. It is one of many ways to visually display a tree,<ref>{{Cite web|url=http://www.spicynodes.org/reference-background.html|title=Spicynodes : Reference Background|website=www.spicynodes.org}}</ref><ref>{{Cite web|url=http://www.visualcomplexity.com/vc/project.cfm?id=26|title=visualcomplexity.com &#124; Radial Tree Viewer|first=Manuel|last=Lima|website=www.visualcomplexity.com}}</ref> with examples dating back to the early 20th century.<ref>{{Cite web|url=http://www.visualcomplexity.com/vc/project.cfm?id=289|title=visualcomplexity.com &#124; Radial Eugenics Diagram|first=Manuel|last=Lima|website=www.visualcomplexity.com}}</ref>  In use, it is a type of [[Information graphics|information graphic]].

[[File:Radial-vs-tri.svg|thumb|middle|upright=1.35|Radial vs. triangular tree layout]]

== Basic layout ==
[[File:Radial-graph-schematic.svg|thumb|upright=0.9|Schematic radial tree]]

The overall distance "d" is the distance between levels of the graph. It is chosen so that the overall layout will fit within a screen. Layouts are generated by working outward from the center, root. The first level is a special case because all the nodes have the same parent. The nodes for level 1 can be distributed evenly, or weighted depending on the number of children they have. For subsequent levels, the children are positioned within sectors of the remaining space, so that child nodes of one parent do not overlap with others.

There are many extensions to this algorithm to create more visually balanced layouts, to allow users to navigate from node to node (changing the center),<ref>Yee, K.-P, D. Fisher, R. Dhamija, & M. Hearst. “Animated Exploration of Dynamic Graphs with Radial Layout”. Proc. Information Visualization, 43-50, 2001.</ref> or accommodate node labels and combine [[Force-based algorithms (graph drawing)|force-directed layouts]] with radial layouts.<ref>Douma, Michael, Greg Ligierko, Ovidiu Ancuta, P. Gritsai, and S. Liu. SpicyNodes: Radial Layout Authoring for the General Public. InfoVis 2009. Atlantic City, NJ. October 2009. Presentation.</ref>

The layout has some similarities to a [[hyperbolic tree]], though a key difference is that hyperbolic trees are based on  [[hyperbolic geometry]], whereas in a radial tree the distance between orbits is relatively linear.

== Comparison to other layouts ==
In a simple case, the first node is at the top, and the linked nodes are beneath. As each node typically has more than one child, the resulting shape is relatively triangular. In a radial layout, instead of each successive generation being displayed a row below, each generation is displayed in a new, outer orbit.

Since the length of each orbit increases with the radius, there tends to be more room for the nodes. A radial tree will spread the larger number of nodes over a larger area as the levels increase. We use the terms level and depth interchangeably.<ref>Greg Book & Neeta Keshary. "Radial Tree Graph Drawing Algorithm for Representing Large Hierarchies." University of Connecticut December 2001</ref> Nevertheless, the number of nodes increases exponentially with the distance from the first node, whereas the circumference of each orbit increases linearly, so, by the outer orbits, the nodes tend to be packed together.

== Examples ==
* [[MindManager]] and [[MindMapper]] are [[Mind map|mindmapping]] systems, which can make radial-like layouts, though are not radial beyond the 2nd level.
* [[SpicyNodes]] was an approach to visualizing hierarchies, which allows moving from node to node.

== See also ==
* [[Radar chart]]

== References ==
{{reflist}}

== External links==
* [http://treevis.net Comprehensive survey and bibliography] of Tree Visualization techniques
* [http://chrisharrison.net/index.php/Visualizations/WikiViz WikiViz: Visualizing Wikipedia] by [[Chris Harrison (computer scientist)|Chris Harrison]]
* [http://www.visualcomplexity.com/vc/search.cfm?input=radial Radial maps at "Visual Complexity" site]

[[Category:Trees (data structures)]]
[[Category:Graph drawing]]