1. James Abello, MSCS Director Computer Science Department Busch Campus
Graph Analyti
Graph Analytics Primer
James Abello, MSCS Director
Computer Science Department
Busch Campus

2. What is a Combinatorial Graph or Network G = (V,E) ?
Collection of Vertices V and “pairs” E of elements from V called Edges.
Ex: V = {a,1,3,b, z}
E = {{a,1}, {b,3}, {z,1}, {a,b}, {a,z} , {b,z} }
Pictorially ?
Graphs can have “weights”, “labels” or “time stamps” on the vertices and edges or more complicated meta-information. Edges may have directions.

3. Examples The Web, The Internet, Phone Calls, Maps,
Co-Occurrence, Paragraphs in Books, Family Trees, Authors and Papers, Airports Flights, Clicks on Web Sites, Friendships networks, Social Media, Biological Networks, Events Collection, Diseases – Symptoms –Treatments, Images(2d,3d), …

4. Graph Sources
News, Scientific Publications, Astronomic Observations, Pictures, Social Events, Biology, Physics, Mathematics, Social Sciences, Health Care Data, Medicine, …

5. A helpful methaphore Effectively and Efficiently
How to go from point a to point b
Effectively and Efficiently

6. Typical Tasks
a. Create or Define Graphs of interest from your Data Sets.
b. Data Access and Graph formation
c. Identify the questions you want to answer
d. Compute Graph Statistics: |V|, |E|, Connectivity, average degree, degree distribution, density, longest paths (Diameter), landmarks, most central vertexes, ….

7. Typical Tasks(cont)
e. Define a “similarity” between the vertices
f. Partition the vertices according to the similarity measure of interest (This has been called “Clustering” or sexier name today is “Unsupervised Learning” )
g. Interpret the clusters

8. Typical Tasks(cont) g. Interpret the clusters
h. (Feedback Loop) Incorporate this information back into your data and run modified algorithms of interest.
i. Summarize the findings, publish or incorporate them into processes of interest.

9. Main Issues Define typical scenarios
b. How is the graph consumed by a user? Text? Visual Interface? On Demand? On a desktop? Special device?
c. What are the interactivity requirements?
d. How can we amplify a human user understanding of the graph data? (maps are good examples of successful stories)
e. How do we access the “satellite” information associated with the graph data?
f. I s the graph and its associated data public?

10. A system at work
An example of current capabilities of graph manipulation systems that are in existence today.
Go to Atlas demo

11. Atlas Local Graph Exploration in a Global Context Fred Hohman
IUI 2019
Fred Hohman
@fredhohman
Georgia Tech
James Abello
Rutgers
Varun Bezzam
Georgia Tech
Polo Chau
Georgia Tech

13. Graph Sensemaking

14. Global View
Graph Sensemaking
Local View

15. Global View
Free Exploration
Graph Sensemaking
Local View
Targeted Exploration

16. Important Structure
Graph Sensemaking
Important Nodes

17. Important Structure
Graph Sensemaking
Important Nodes

18. Important Structure
Graph Sensemaking
Important Nodes

19. HCI Human-computer Data Mining Interaction Automatic
User-driven, iterative
Summarization, clustering, classification
Interactive, visualization
Millions of nodes
Thousands of nodes

20. HCI Human-computer Data Mining Interaction Automatic
User-driven, iterative
Summarization, clustering, classification
Interactive, visualization
Millions of nodes
Thousands of nodes
The Ubiquity of Large Graphs and Surprising Challenges of Graph Processing. Sahu, et al. VLDB, 2017.

21. HCI Human-computer Data Mining Interaction Automatic
User-driven, iterative
Summarization, clustering, classification
Interactive, visualization
Millions of nodes
Thousands of nodes
The Ubiquity of Large Graphs and Surprising Challenges of Graph Processing. Sahu, et al. VLDB, 2017.

22. 12

23. Atlas interactive graph exploration via scalable edge decomposition
bit.ly/atlas-iui
interactive graph exploration via
scalable edge decomposition 13

24. Atlas interactive graph exploration via scalable edge decomposition
bit.ly/atlas-iui
interactive graph exploration via
scalable edge decomposition
separate graph into graph layers 13

25. Atlas interactive graph exploration via scalable edge decomposition
bit.ly/atlas-iui
interactive graph exploration via
scalable edge decomposition
separate graph into graph layers
reveal peculiar subgraph 13

26. Atlas interactive graph exploration via scalable edge decomposition
bit.ly/atlas-iui
interactive graph exploration via
scalable edge decomposition
separate graph into graph layers
reveal peculiar subgraph
visualize local + global structure 13

28. 1 3 4 5 1 5 4 1 2 2

29. peel = 1 1 3 4 5 1 5 4 1 2 2

30. peel = 1 3 4 2 5 4 2

31. peel = 2 3 4 2 5 4 2

32. peel = 2 3 3 3 3

33. peel = 3 3 3 3 3

34. peel = 3 3
3 3 3 3 3

35. peel = 1 1 1 5 1 2 1 1 2 2

36. peel = 1 1 2

37. peel = 1 2

38. peel = 2 2

39. peel = 2 2

40. peel = 1 1 1 5 1 1 1

41. peel = 1 1 1 1 1 1

42. 3 1 1
3 3 1 3 3 1 1 2 3 2

43. graph layer 3
graph layer 1 1 3
3 3 1
graph layer 2 2 1 1 3 2

44. graph layer 3 graph layer 1 graph layer 2 vertex clones 1 3 3 3 1 2 1
3 3 1
graph layer 2 2 1 1 3
vertex clones 2 2

45. Graph Vertices Edges Time (s) Layers Google+ 24K 39K ~0 10
arXiv astro-ph
19K
198K 47
Amazon
335K
925K 6
US Patents
3.8M
17M 11 41
Wikipedia (German)
3.2M
82M
225
320
Orkut
3.1M
117M 92 91 32

46. Time complexity: O(#edges x #layers)
Graph
Vertices
Edges
Time (s)
Layers
Google+
24K
39K ~0 10
arXiv astro-ph
19K
198K 47
Amazon
335K
925K 6
US Patents
3.8M
17M 11 41
Wikipedia (German)
3.2M
82M
225
320
Orkut
3.1M
117M 92 91
Time complexity: O(#edges x #layers)
layers << edges 32

47. Scalable K-Core Decomposition for Static Graphs Using a Dynamic Graph Data Structure
Alok Tripathy, Fred Hohman, Duen Horng (Polo) Chau, Oded Green
IEEE International Conference on Big Data. Seattle, WA, USA, 2018. 33

48. GPU + dynamic graph data structure -> 4x - 8x speed up over ParK
Scalable K-Core Decomposition for Static Graphs Using a Dynamic Graph Data Structure
Alok Tripathy, Fred Hohman, Duen Horng (Polo) Chau, Oded Green
IEEE International Conference on Big Data. Seattle, WA, USA, 2018.
GPU + dynamic graph data structure
-> 4x - 8x speed up over ParK 33

49. Demo: Understanding Word Embedding Graph
Nodes: 66K words from Wikipedia
Edges: 214K (connect words with small distance)
families of birds
caeciliidae
caeciliidae worm-like amphibians
families of sea snails 34

52. User Study
Goal: use Atlas to spot interesting patterns, mimicking their own work
Graph Analysts
Researcher, Symantec
Graphs
Yelp Reviews Network
Researcher, NASA Systems engineer, NASA
All PhDs + use graphs daily or weekly
SEC Insider Trading Graph GloVe Word Embed. Graph
Intro questionnaire → Atlas tutorial → Study → Exit questionnaire

53. User Study Findings 38

54. User Study Findings
3D for overview, 2D for details 38

55. User Study Findings 3D for overview, 2D for details
3D useful for intro to new data → get a “feel” for the graph 38

56. User Study Findings • 3D for overview, 2D for details
3D useful for intro to new data → get a “feel” for the graph Graph Ribbon + Layers view used more precisely 38

57. User Study Findings • 3D for overview, 2D for details
3D useful for intro to new data → get a “feel” for the graph Graph Ribbon + Layers view used more precisely
Show nearest neighbors used frequently 38

58. User Study Findings • 3D for overview, 2D for details
3D useful for intro to new data → get a “feel” for the graph Graph Ribbon + Layers view used more precisely
Show nearest neighbors used frequently
Identifying and linking meaningful graph substructures 38

59. User Study Findings • 3D for overview, 2D for details
3D useful for intro to new data → get a “feel” for the graph Graph Ribbon + Layers view used more precisely
Show nearest neighbors used frequently
Identifying and linking meaningful graph substructures
Vertex clones as traversal mechanism between layers 38

60. User Study Findings • 3D for overview, 2D for details
3D useful for intro to new data → get a “feel” for the graph Graph Ribbon + Layers view used more precisely
Show nearest neighbors used frequently
Identifying and linking meaningful graph substructures
Vertex clones as traversal mechanism between layers
Application to anomaly detection 38

61. User Study Findings • 3D for overview, 2D for details
3D useful for intro to new data → get a “feel” for the graph Graph Ribbon + Layers view used more precisely
Show nearest neighbors used frequently
Identifying and linking meaningful graph substructures
Vertex clones as traversal mechanism between layers
Application to anomaly detection
“…analysis (using [both] vertex clones and layers) naturally reveals potentially anomalous substructures and vertices. This is highly useful from a cybersecurity perspective.” 38

62. Future Work

63. Future Work
Automatically suggest interesting layers

64. Future Work •
Automatically suggest interesting layers Dynamic graph decomposition visualization

65. Future Work •
Automatically suggest interesting layers Dynamic graph decomposition visualization
Visual scalability (e.g., super-noding, edge bundling, graph motif)

66. Atlas bit.ly/atlas-iui Local Graph Exploration in a Global Context
Thanks!
Fred Hohman
@fredhohman
James Abello
bit.ly/atlas-iui
families of birds
Varun Bezzam
caeciliidae
caeciliidae worm-like amphibians
Polo Chau
families of sea snails
families of land creatures
caeciliidae
We thank the anonymous reviewers for their constructive feedback.