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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 screen with limited pixels High computational cost Interaction Show more detail for area of interest

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a survey on graph visualization
A Survey on Graph Visualization

Presented by

Yang Zhang

Dave Fuhry

challenges
Challenges
  • Graph Layout
    • Make a concrete rendering of graph.
  • Scale for large graphs
    • Render on a computer screenwith limited pixels
    • High computational cost
  • Interaction
    • Show more detail for area of interest
    • Exploration for intuition
force directed layout
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
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 and pan
    • Zoom for graphs exact, adjustment of screen transformations
  • The internet map: http://internet-map.net/
hierarchical clustering
Hierarchical Clustering
  • Successively applying the clustering process to clusters discovered by a previous step.
  • Can be navigated as tree
dynamic graphs
Dynamic Graphs

Events in dynamic graphs

visualizing cohesive subgraphs
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
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
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
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