graph visualization

Graph Visualization: A Survey

Overview Applications, Key Issues Graph Layout Navigation and Interaction Clustering Systems Current State of Graph Visualization

ReferenceI.Herman, G. Melancon, M.S. Marshall, Graph Visualization and Nav-igation in Information Visualization: A Survey, IEEE Transactions onVisualization and Computer Graphics, Volume 6(1), January, 2000.ITCS 6010/8010: Information Visualization 1 Graph Visualization

Graph Visualization

Survey is focused on the use of graph visualization techniques toproblems in Information Visualization.

Graphs - a natural way to represent relationships. Graphs in Infoviz: Are there inherent relationships among the input

data elements? NO: Unstructed Data - Infoviz must be used to discover relation-

ships. YES: Graphs can be used to represent the relationships - data

elements (nodes) and edges (relationships). Survey is focused on structured data and the use of graphs applied

to Infoviz domain.

ITCS 6010/8010: Information Visualization 2 Graph Visualization

Applications

File hierarchies, organization charts, biological taxonomies Web site maps, browsing history Biology: Evolutionary, phylogenetic trees, genetic maps, biochemi-

cal pathways, protein function Computer Science: data structures, object oriented systems, ER

diagrams, scene graphs (graphics)


Key Issues in Graph Visualization

Size is the key issue in visualizing graphs. Large graphs are constrained by display resources, and usability

(interaction, for instance) Very little work on applying cognitive science or human factors.


Graph Layout Algorithms

Background: Graph DrawingGiven a set of nodes and a set of edges (relations), calculate the positionof the nodes and the curve to be drawn for each edge. Well studied subject (hundreds of publications, books!) Planarity: Graphs drawn on a plane with no edge crossing Layout types: grid layouts (nodes at integer coords), force-directed

models, simulated annealing based layouts. Aesthetic Issues: Nodes, edges evenly distributed, isomorphic sub-

structures, straight line edges, etc.


Example Tree Layout

Reingold and Tilford Algorithm

Isomorphic subtrees are always laid out the same way Distance between nodes is a parameter.ITCS 6010/8010: Information Visualization 6 Graph Visualization

Layout Algorithm Issues

Size: Graphs with thousands of nodes can make most layout algo-rithms almost useless.

NicheWorks, H3Viewer are among systems that can handle largegraphs.

High Node Density: Traditional algorithms cannot scale up, makinginteraction difficult.

Can also use 3D layouts or non-Euclidean geometry. Extremely large graphs - need methods to simplify (reduce) graph

size (clustering, grouping)


Layout Algorithm Issues (contd) Predictability: Consecutive runs of an algorithm should not result in

radically different visual representations (preserving mental map) Time Complexity: Real-time (or near real-time) updates of the graph

is needed in highly interactive applications, where the graph can bemodified.


Traditional Layout

Child nodes below common ancestor Reingold and Tilford algorithm - the best known - can produce top-

down or lef to right layouts, as well as grid positioning. H-Tree: Representation for binary trees; uses axis-aligned repre-

sentaton of edges. Radial Trees (Eades) Balloon Views - planarized Cone Trees Tree maps, Onion Graphs, Cushion Treemaps

ITCS 6010/8010: Information Visualization 9 Graph Visualization ITCS 6010/8010: Information Visualization 10 Graph Visualization


Traditional Layout (contd) Spring Layouts: or force-directed Models nodes and edges as physical bodies tied with springs. Uses Hookes law to define forces between bodies Can lead to well balanced layouts, some optimzed for minimizing

edge crossings and predictable layouts. Disadvantage: Computational complexity is generally O(N 3),

most methods are highly unpredictable.


Spanning Trees

Most traditional layout algorithms work well on small graphs A practical solution is to layout the graph by computing the spanning

tree (tree layouts are typically of O(N) complexity). Once the tree is laid out, the other edges can then be added to tree. Methods: Can use breadth-first or depth-first search, starting from a likely

root node. If edges have weight, can use various optimization criteria (and

heuristics) in the layout algorithm


3D Layouts

3D layouts, in combination with interactive viewing can accommo-date larger graphs, while compensating for occlusion

Most force-directed and simulated annealing approaches can alsobe extended to 3D.

3D layouts also use visual cues such as transparency, depth queu-ing, etc.

Classic Example: Cone Trees (a direct 3D algorithm) and their ex-tensions (disk trees)


3D Radial Layout


Cone Trees


Other 3D Layout Examples

SGI file system navigator (until version 5) (seen in Jurassic Park!) Perspective Wall - data representation as posters on large walls Viznet, Vitesse - data mapped onto a sphere

Difficulties with 3D layouts 3D navigation in 2D displays and 2D input devices VR and immersive environments are not commonplace


Hyperbolic Layouts

Provides a distorted view of a tree in 2D or 3D, similar to fish-eyeviews

Makes it possible to view and interact with large trees, and thus cru-cial for real-life Infoviz applications.

A mapping from hyperbolic to Euclidean space - two models, Kleinand Poincare.


Hyperbolic Layouts(contd) Klein Model: Klein model uses an open disc (sphere in 3d) as a subset -

hyperbolic plane contains points internal to the disc Line segments of equal length in hpyerbolic plane get exponen-

tially smaller as they approach the perimeter Poincare Model: Similar to the Klein model, but segments are arcs,

intersecting orthogonally at the perimeter of the disc.


Hyperbolic Layouts(contd)




The small wedges seen in Euclidean plane (resulting in unusablelayouts is very different in the hyperbolic plane (wedges are openedup)


Navigation and Interaction

Crucial tools to dealing with large graphs Can help reveal graph structure Real-time interaction is an important goal.


Zoom and Pan

Standard graphics interaction operations, manipulated by affinetransformations, followed by a redraw.

Geometric zoom vs. Semantic Zoom. Zooming in, can cause loss of context


Space-Scale Diagrams

Represent points in image as rays (with point, magnification) Choose paths to destination as a combination of zoom and pan ac-

tions


Focus+Context Techniques

Techniques that allow users to focus on some detail of the visualization,without losing context.Fisheye Distortion Simple distortions use a radial function, for eg.,

h(x) = (d + 1)/(d + 1/x)


Fisheye Distortion(contd)


Fisheye Distortion(contd)


Fisheye Distortion(contd) Cartesian Fisheye: Distortion applied to X and Y independently. Approximation of segments with linear elements can introduce edge

crossings.


Focus+Context and Layout

Fisheye distortion is typically a processing step separate from thelayout.

Hyberbolic layout is the exception, as the technique is designed withthe goal of focus+context.

Hyperbolic layouts - changing focus is equivalent to changing thecenter of the Euclidean circle(sphere).

Other Examples: mapping onto spheres and ellipsoids, followed byperspective projection, Perspective Wall.


Clustering

Advantageous to reduce the number of elements displayed, espe-cially very large graphs/trees.

Structure-based clustering: uses only structural information aboutthe graph

Content-based clustering: node and edge attributes are used to de-termine clusters.

Most clustering work is structure based. Clustering - used to accomplish filtering and search.


Clustering Approaches

Locate disjoint clusters (simpler to navigate) Choose clusters with the least number of edges between members

(Ratio-Cut technique) Hierarchical clustering


Cluster Layout

Can just layout the clusters by themselves - good high level view ofthe graph structure

Use glyphs to represent clusters and treat them as supernodeswith abridgemens between clusters.

Force-directed cluster layout: nodes that are related to each otherare attracted, while all nodes have a minimal repulsion force (O(N 3)complexity).


Node Metrics for Clustering

Structure or content based. Combination of structure and content based metrics are more pow-

erful, eg. linear weighted combination. Representation of unselected nodes Ghosting - deemphasizing nodes Hiding Grouping - grouping under a new super-node representation


Cluster Representation


Graph Drawing - Systems, Journals,Conferences

A very large community of researchers, users Large number of systems have been implemented Graph Drawing Symposia - dedicated to this domain Journal of Graph Algorithms and Applications Significant ties to CHIXX, UISTXX, InfoVizXX, IEEE TVCG, CG

Forum


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graph visualization