A Survey on Graph Visualization

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# A Survey on Graph Visualization - PowerPoint PPT Presentation

A Survey on Graph Visualization. Presented by Yang Zhang Dave Fuhry. Challenges . Graph Layout Make a concrete rendering of graph. Scale for large graphs Render on a computer screen with limited pixels High computational cost Interaction Show more detail for area of interest

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A Survey on Graph Visualization

Presented by

Yang Zhang

Dave Fuhry

Challenges
• Graph Layout
• Make a concrete rendering of graph.
• Scale for large graphs
• Render on a computer screenwith limited pixels
• High computational cost
• Interaction
• Exploration for intuition
Force-Directed Layout
• Nodes are modeled as physical bodies that are connected through springs (edges)
• Pseudo code
• Example
• High running time
• The typical force-directed algorithms are in general considered to have a running time equivalent to O(n3) , where n is the number of nodes of the input graph.
Pseudo Code

set up initial node positions randomly

loop

total_kinetic_energy := 0

for each node

net-force := (0, 0)

for each other node

net-force := net-force + repulsion( this_node, other_node )

for each spring connected to this node

net-force := net-force + attraction( this_node, spring )

// without damping, it moves forever

this_node.velocity := (this_node.velocity + timestep * net- force) * damping

this_node.position := this_node.position + timestep * this_node.velocity

total_kinetic_energy := total_kinetic_energy + this_node.mass *(this_node.velocity)^2

until total_kinetic_energy is less than some small number // the simulation has stopped moving

Zoom and pan
• Zoom for graphs exact, adjustment of screen transformations
• The internet map: http://internet-map.net/
Hierarchical Clustering
• Successively applying the clustering process to clusters discovered by a previous step.
• Can be navigated as tree
Dynamic Graphs

Events in dynamic graphs

Visualizing Cohesive Subgraphs
• cohesive subgraphs
• A subgraph in which vertices are densely connected.
• Clique, K-Core, etc.
• CSV
• For each edge e, compute c(e), which is the size of the biggest clique that contains e.
• Plot each vertex in the following order:
• Randomly pick up the first vertex to plot;
• Pick up the next vertex which shares an edge with maximum c(e) with previously plotted vertices. Plot the vertex with height = c(e)
• The peaks indicate dense cohesive subgraphs
Directed K-Core : D-core
• D = (V;E) is a digraph that is a set V of vertices and a set E of directed edges between them.
• The min-in-degree and the min-out-degree of a digraph D are defined as
• a (k; l)-D-core of D is a maximal sub-digraph F of D where
• Denoted as
D-core matrix
• For directed graph D, there is a unique (k; l)-D-core for each (k; l). We define D-core matrix AD as follows:

AD(k; l) = size of (k; l)-D-core.

Tools

Web-based tools

• Cobweb: http://bioinformatics.charite.de/cobweb/
• Sigma.js: http://sigmajs.org/
• InfoVis: http://thejit.org/
• Cytoscape web: http://cytoscapeweb.cytoscape.org/

Applications

• Gephi: http://gephi.org/
• Cytoscape: http://www.cytoscape.org/
• Guess: http://graphexploration.cond.org/index.html