Node-Attribute Graph Layout for Small-World Networks Helen Gibson Principal Supervisor: Dr. Paul Vickers 1 st Supervisor: Dr. Maia Angelova 2 nd Supervisor: Dr. Fouad Khelifi Previous Supervisor: Dr. Joe Faith

What is a Graph? 2 Relationships between concepts Mathematics and Graph Theory Graph Graph Drawing Information Visualisation Network Network Visualisation

Examples 3 Social Networks Biological Networks World Wide Web IP Addresses

What’s the Problem? Yeast interaction network in Gephi 4 It looks nice but is it doing anything useful? Typical complaint: Giant-Hairball Caused by force-directed algorithms Old, but still popular and most commonly used Connected nodes attract, other repel

How Can This Be Solved? 5 Node Attributes Example – Social Network Node = People Links = Friendships Attributes = age, gender, location, games they interact with, pages they had liked etc. Typical Usage – As retinal variables Use to tell us more information about the graph Uses beyond retinal variables?

Research Aims 6 Novel graph layout based on node-attributes Many node attributes -> use a dimension reduction technique Visual analysis of graphs Visual Analytics - the science of analytical reasoning facilitated by interactive visual interfaces. [Thomas and Cook, 2005] To further understand the connectivity and structure of the graph

Node-Attributes to Dimensions 7 Attributes as a second set of links Nodes Attributes Each attribute node is a dimension and existence of a link is a value for that dimension on that node

Dimension Reduction and TPP 8 In visualisation:  Many variables form a high-dimensional space reduce to 2 or 3 dimensions that can be seen on a display.  Linear projections Projection Pursuit:  Finds the most ‘interesting’ projection  Interestingness depends on the data Targeted Projection Pursuit (TPP):  Interactive  Searches for a projection closest to a users desired view  In following case, separation of the clusters as far as possible.

Small-World Networks 9 Networks that are:  Highly clustered  Smaller than average shortest path length An Example:  4 clusters  Small nodes are attributes Clustering – users’ most valued layout feature

Force-Directed Graph+TPP 10 Comparison

What’s Next? 11 ‘How much better is the clustering?’ Real world domain applications What do we learn about the data from the layout? Evaluation

Publications 12 Gibson, H. (2010) Data-driven layout for the visual analysis of networks. GROUP28: The XXVIII International Colloquium on Group-Theoretical Methods in Physics. Newcastle-upon-Tyne, July Poster presentation. Gibson, H., Faith, J. (2011) Node-attribute graph layout for small-world networks. 15 th International Conference on Information Visualisation. London, July 2011