A Survey on Graph Visualization 1 Presented by Yang Zhang Dave Fuhry

Challenges 2 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

Force-Directed Layout Nodes are modeled as physical bodies that are connected through springs (edges) – Pseudo code Pseudo code – Example Example High running time – The typical force-directed algorithms are in general considered to have a running time equivalent to O(n 3 ), where n is the number of nodes of the input graph. 3

Pseudo Code 4 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:

Hierarchical Clustering Successively applying the clustering process to clusters discovered by a previous step. Can be navigated as tree

Example: ASK-GraphView 7

Dynamic Graphs Events in dynamic graphs

Event-View Interface 9

Event Visualization 10

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 11

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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.

Tools Web-based tools Cobweb: Sigma.js: InfoVis: Cytoscape web: Applications Gephi: Cytoscape: Guess: 15