1. Force Directed Layouts Hank Childs, University of Oregon November 22nd, 2013

2. Upcoming Schedule • 11/21: alternate lecture #1 (force directed layouts) • 5pm, Deschutes 220 • 11/22: uncertainty visualization (KP) • 12/2: alternate lecture #2 (force directed layouts) • 2pm, HEDCO 142 • 12/4: medical visualization (Erik Anderson) • 12/6: unstructured grids • Faculty fireside (parallel visualization): • Week of 12/2 or week of 12/9 • Final: Thurs 12/12, 3:15PM, Rm 220

3. Undirected graphs • G = (V, E) • V: set of vertices • E: set of edges, (a,b), where a,b in V • Possible: weights • Weights on edges • Weights on vertices

4. Inspiration: LinkedIn Maps

5. Inspiration: LinkedIn Maps

6. Inspiration: LinkedIn Maps Positive aspects: Related nodes are near each other Aesthetically pleasing Is this a good graph? Why or why not?

7. Aesthetic Considerations • Crossings – minimize towards planar • Total edge length – minimize towards proper scale • Area – minimize towards efficiency • Maximum edge length – minimize longest edge • Uniform edge length – minimize variance • Total bends – minimize orthogonal towards straight-line Slide c/o: R. Maciejewski, ASU Some details from this slide borrowed from John Stasko’sGraph lecture: http://www.cc.gatech.edu/~stasko/7450/Notes/graph1.pdf

8. What is the source data? • LinkedIn: • I send you a LinkedIn request, or you send me a LinkedIn request. • Data: • a list of people • a list of people they are connected to • LinkedIn Maps: • only consider connections to my connections • if I am connected to person X, and they are connected to Y, and I am not connected to Y, then just ignore Y

9. How is LinkedIn data converted to graphs? • Let P be the list of my connections • I have an edge to every one of my connections • (hank, q) for all people q in P • Create edge (x,y) if x and y are in P and x is connected to y • Edge weights: number of shared connections between x and y (“Good” = related nodes close to each other, aesthetically pleasing) Given data like this, how can we make a “good” graph?

10. Force-directed layouts • Common information visualization algorithm • Not clear this is the algorithm LinkedIn Maps is using • Still graph G = (V, E), vertices V, edges E • Still edge weights on E • Goal: edges are more or less of equal distance, as few crossing edges as possible

11. Force-directed layouts: idea • Two competing forces: • Edges become springs • pull vertices together • Hooke’s law • Vertices become electric particles • push vertices apart • Coulomb’s law

12. Force-directed layouts: idea • Place vertices in random initial position • Iteratively change vertex positions based on forces • This iterative process ultimately converges, in a way that minimizes energy (over both spring & electric repulsion) • If it doesn’t converge add dampening factor • The final position of the vertices is the force-directed layout

13. Interactivity Use Cases • Watching the graph converge • Modifying a graph after convergence • Just modify layout • http://bl.ocks.org/mbostock/1062288 • Associate two vertices together more closely • Set constraints (sticky layout) • http://bl.ocks.org/mbostock/3750558

14. Force-directed layouts: problem • Updating vertex v_i requires considering forces from v_1, v_2, … v_n, as well as all edges incident to v_i. • Result is O(n^2) work per iteration • Number of iterations estimated as O(n) • Total work is O(n^3) This becomes very expensive when n > 1000

15. Algorithms for improved performance • Overlaps with physics: n-body particle equations • Multiple approaches • Barnes-Hut • When considering one vertex, minimize # of other vertices considered • Drops to O(n*log(n)) per iteration, O(n^2*log(n)) overall • Depends on quadtree data structure

16. Octree • Source: wikipedia

17. Quadtree • Source: wikipedia

18. Barnes-Hut • Divide graph into quadtree • Iterate over each vertex. • Do NOT consider Coulomb effects for all other vertices • Instead: • group vertices in distant quad tree cells together • consider these vertices as a single vertex (with a higher mass) •  less vertices considered Intuition on why this works: the close ones are most important and they are still considered individually

19. Gephi • Gephi: open-source network analysis and visualization software package • Maintained by French non-profit (Gephi Consortium) • Written in Java on the NetBeansplatform • Example usages: • Twitter network traffic • Network analysis We will look at relationships in “Les Miserables” using data set compiled by Donald Knuth.

20. Les Miserables

21. Les Miserables Movie Jean Valjean Cosette Javert Fantine Marius Thenardiers + many others, including revolutionaries, priests & nuns, prisoners, criminals, policemen

22. Demonstration • (Now Gephi demonstration with Samuel Li)