Title: H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space
1H3 Laying Out Large Directed Graphs in 3D
Hyperbolic Space
- Andrew Chan
- CPSC 533C
- March 24, 2003
2H3
Image from http//graphics.stanford.edu/papers/h3
/fig/nab0.gif
3Ideas behind H3
- Creating an optimal layout for a general graph is
tough - Creating an optimal layout for a tree is easier
- Often it is possible to use domain-specific
knowledge to create a hierarchical structure from
a graph
4Stumbling Blocks
- The deeper the tree, the more nodes exponential
growth - You can see an overview, or you can see fine
details, but not both
5Solution
- A layout based on hyperbolic space, that allows
for a focus context view - H3 used to lay out hierarchies of over 20 000
nodes
6Related Work
- H3 has its roots in graph-drawing and
focuscontext work
72D Graph and Tree Drawing
- Thinking very small-scale
- Frick, Ludwig, Mehldau created categories for
graphs of nodes ranged from 16 in the smallest
category, to gt 128 in the largest
82D Tree Drawing (contd)
MosiacG System Zyers and Stasko Image
from http//www.w3j.com/1/ayers.270/paper/270.htm
l
93D Graph Drawing
SGI fsn file-system viewer Image
from http//www.sgi.com/fun/images/fsn.map2.jpg
103D Graph Drawing (contd)
- Other work centered around the idea of a
mass-spring system - Node repel one another, but links attract
- Difficulty in converging when you try to scale
the systems - Aside Eric Brochu is doing similar work in 2D -
http//www.cs.ubc.ca/ebrochu/mmmvis.htm
113D Tree Drawing
Cone Trees, Robertson, Mackinlay, Card Image
from http//www2.parc.com/istl/projects/uir/pubs/
items/UIR-1991-06-Robertson-CHI91-Cone.pdf
12Hyperbolic FocusContext
Hyperbolic Tree Browser, Lamping, Rao Image
from http//www.acm.org/sigchi/chi95/Electronic/d
ocumnts/papers/jl_figs/strip1.htm
13Alternate Geometry
- Information at http//cs.unm.edu/joel/NonEuclid/
- Euclidean geometry
- 3 angles of a triangle add up to?
- Shortest distance between two points?
- Spherical geometry
- How we think about the world
- Shortest way from Florida to Philippines?
14Alternate Geometry (contd)
- Hyperbolic Geometry / Space
- Is important to the Theory of Relativity
- The fifth dimension
- Can be projected into 2-D as a pseudosphere
- Key As a point moves away from the center
towards the boundary circle, its distance
approaches infinity
15H3s Layout
Image from http//graphics.stanford.edu/papers/h3
/fig/nab0.gif
16Finding a Tree from a Graph
- Most effective if you have domain-specific
knowledge - Examples
- File system
- Web site structure
- Function call graphs
17Tree Layout
Cone tree layout versus H3 Layout Image from
http//graphics.stanford.edu/papers/h3/html/node12
.htmconefig
18Sphere Packing
- Need an effective way to place information
- Cannot place spheres randomly
- Want to have a fast algorithm
19Sphere Packing (contd)
Image from http//graphics.stanford.edu/papers/h3
/fig/incrhemi.gif
20Demo
21Strengths
- Can easily see what the important structures are
and the relationships between them - Can let you ignore noise in data
- Animated transitions
- Responsive UI
22Weaknesses
- Starting view only uses part of the sphere
- Moving across the tree can disorient you cost of
clicking on the wrong place is high - Labels not present if node too far from center
23Questions?