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A Survey on Graph Visualization

Presented byYang ZhangDave Fuhry

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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– Exploration for intuition

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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.

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Pseudo Codeset 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

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Example: ASK-GraphView

Dynamic GraphsEvents in dynamic graphs

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Event-View Interface

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Event Visualization

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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

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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.

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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