This document discusses analyzing graphs and networks with Python. It provides examples of using graphs to study political polarization on Twitter and correlation graphs. It defines network terminology and describes properties of complex networks like power law distributions, small world phenomena, and high clustering coefficients. Finally, it discusses tools for graph analysis in Python like NetworkX and graph-tool and graph analysis techniques such as centrality measures, community detection, and network visualization.

1. Find insights in graphs
with Python

2. Ego network

3. Ego network

4. Ego network

5. Ego network
КПИ
Data Science

6. Political Polarization on TwitterExamples
Political Polarization on Twitter
retweet network mention network

7. Correlation Graphs
Examples
https://www.oreilly.com/ideas/ideas-on-interpreting-machine-learning

8. Examples
https://voxukraine.org/longreads/committees/article-ua.html

9. Terminology
network = graph
nodes = vertices, actors
links = edges, relations
clusters = communities
directed
undirected

10. Complex networks
• not regular, but not random
• non-trivial topology
• universal properties
• everywhere

11. Complex networks
1. Power law node degree distribution
”scale-free” networks
2. Small diameter and average path length
”small world” networks
3. Hight clustering coefficient

12. 1. Power law
D.Price, 1965
Power law node degree distribution

13. 2. Six degrees of separation
Any two people are on average separated no more that by six
intermediate connections
L.Backstrom, 2012

14. 3. Triadic closure
If A and B and B and C are strongly linked, the the tie between B and C is
always present
high clustering coefficient
high transitivity
Grannoveter, 1973

15. Relationship graph
The links of Love

16. Tools
igraphNetworkX
pure Python
graph-tool
Python, R, C Python (C)
API ++ +++ +
speed ++ +++
documentation +++ + +++
dynamic networks +++ + ++

17. Performance comparison
https://graph-tool.skewed.de/performance

19. Graph formats
igraph
NetworkX
graph-tool

20. Graph formats
igraph
NetworkX
graph-tool

21. GRAPHS ARE COMING

22. Network of Thrones

23. «important» nodes
clusters
visualisation

24. Notations

25. Degree centrality

27. Closeness centrality

29. Betweenness centrality
g.betweenness()

31. Eigenvector centrality

32. Erik Bernhardsson

33. Go
Erik Bernhardsson

35. Page Rank

37. Edge betweenness

38. Edge betweenness
cut

39. Modularity

40. Fast community unfolding
V. Blondel et.al., 2008

41. Walktrap
P. Pons and M. Latapy, 2006

43. Pipeline
Preprocess
Top Nodes
Communites Visualization
Filter
Data

44. Demo