Clustered graph, visualization, hierarchicalvisualization

Nathalie Villa-Vialaneix

http://www.nathalievilla.org

SAMM (Université Paris 1)

2012/02/21 - Dagstuhl seminar 12081

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 1 / 4

Full vs simplified visualizationFramework: Static graph visualization.Standard (FDP) approach: visualize the whole graph

aims at being aesthetic⇒ tends to place the hubs in the center of thefigure (edges with uniform length); does not emphasize dense groups

Simplified approach: find communities and represent each one by aglyph

and investigate sub-structure by a hierarchical clustering

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 2 / 4

Full vs simplified visualizationFramework: Static graph visualization.Simplified approach: find communities and represent each one by aglyph

and investigate sub-structure by a hierarchical clustering

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 2 / 4

Full vs simplified visualizationFramework: Static graph visualization.Simplified approach: find communities and represent each one by aglyph and investigate sub-structure by a hierarchical clustering

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 2 / 4

Basic description1 Search for communities: node clustering (e.g., modularity

optimization)

2 Iterate the clustering in each class in a hierarchical way.3 Visualize the graph (in a simplified way) at various levels of the

clustering hierarchy.

Include information about the quality of the clustering in therepresentation? (user warning)

Example: Color and weight edgesbetween clusters according to theircontribution to the modularity

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

Basic description1 Search for communities: node clustering (e.g., modularity

optimization)

Is the clustering relevant / significant?

2 Iterate the clustering in each class in a hierarchical way.3 Visualize the graph (in a simplified way) at various levels of the

clustering hierarchy.

Include information about the quality of the clustering in therepresentation? (user warning)

Example: Color and weight edgesbetween clusters according to theircontribution to the modularity

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

Basic description1 Search for communities: node clustering (e.g., modularity

optimization)

Is the clustering relevant / significant?Possible answer: generate N random graphs with the same degreedistribution and compare the observed optimal modularity to theoptimal modularity distribution among the N random graphs

2 Iterate the clustering in each class in a hierarchical way.3 Visualize the graph (in a simplified way) at various levels of the

clustering hierarchy.

Include information about the quality of the clustering in therepresentation? (user warning)

Example: Color and weight edgesbetween clusters according to theircontribution to the modularity

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

Basic description1 Search for communities: node clustering (e.g., modularity

optimization)2 Iterate the clustering in each class in a hierarchical way.

When to stop the process? Is the clustering relevant /significant?

3 Visualize the graph (in a simplified way) at various levels of theclustering hierarchy.

Include information about the quality of the clustering in therepresentation? (user warning)

Example: Color and weight edgesbetween clusters according to theircontribution to the modularity

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

Basic description1 Search for communities: node clustering (e.g., modularity

optimization)2 Iterate the clustering in each class in a hierarchical way.3 Visualize the graph (in a simplified way) at various levels of the

clustering hierarchy.

Include information about the quality of the clustering in therepresentation? (user warning)

Example: Color and weight edgesbetween clusters according to theircontribution to the modularity

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

Basic description1 Search for communities: node clustering (e.g., modularity

optimization)2 Iterate the clustering in each class in a hierarchical way.3 Visualize the graph (in a simplified way) at various levels of the

clustering hierarchy.

How to have consistent representations? (a cluster and itssubclusters are approximately displayed at the same place) How totake into account the space needed for a cluster of the last level of thehierarchy in any representation (at any level)?

Include information about the quality of the clustering in therepresentation? (user warning)

Example: Color and weight edgesbetween clusters according to theircontribution to the modularity

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

Basic description1 Search for communities: node clustering (e.g., modularity

optimization)2 Iterate the clustering in each class in a hierarchical way.3 Visualize the graph (in a simplified way) at various levels of the

clustering hierarchy.

How to have consistent representations? (a cluster and itssubclusters are approximately displayed at the same place) How totake into account the space needed for a cluster of the last level of thehierarchy in any representation (at any level)?Possible solution: Recursively estimate the place needed for eachcluster in the hierarchy (by a circle encompassing the visualization of

all sub-clusters)⇒ over-estimation

Include information aboutthe quality of the clustering in the representation? (user warning)

Example: Color and weight edgesbetween clusters according to theircontribution to the modularity

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

Basic description1 Search for communities: node clustering (e.g., modularity

optimization)2 Iterate the clustering in each class in a hierarchical way.3 Visualize the graph (in a simplified way) at various levels of the

clustering hierarchy.

Include information about the quality of the clustering in therepresentation? (user warning)

Example: Color and weight edgesbetween clusters according to theircontribution to the modularity

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

Open issues

• Clustering: what is a meaningful clustering? When to stop thehierarchy?

• Clustering hierarchy representation: how to anticipate, at a givenlevel, the place needed for the representation of the finest levels?

• Including estimation about the clustering quality in therepresentation: at the node level (“quality” of the clustering for thecluster? What does that mean?) or at the edge level (contribution tothe modularity between clusters?)

Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 4 / 4