This document provides an overview of social network analysis, including what social networks are, what can be learned from analyzing social networks, and how social network analysis can be performed. Some key findings that can be uncovered include the six degrees of separation principle, the 80-20 rule of social popularity where a minority of nodes have most connections, how to identify influential nodes, and how to group similar nodes into communities. Various metrics and models are described for analyzing features like path lengths, degree distributions, ranking nodes, measuring community structure, and more. Examples of social network analysis are also provided.

1. Social Network Analysis
What it is, what we can learn from it, and how we
can do it

2. Backstrom & Kleinberg, 2014

3. Predict your partner
1.3m users in a relationship, 379m people,
8.6b connections

4. Predict your partner
1.3m users, 379m people, 8.6b connections
Accuracy: 60%

5. Andris et al., PLoS ONE, 2015

6. What is it?

10. Social networks connect people

11. Social network
A social structure that represents the
relationships between people

12. Social network
A graph model that represents the dyadic
relationships between people

14. Nodes and Edges

15. Nodes and Edges

16. Nodes and Edges

17. Nodes and Edges

19. Network
A graph model that represents the dyadic
relationships between entities

21. Ahn et al.,Sci. Rep., 2011

22. Weighted network
Links can have a weight

23. Directed network
Links can be directed

24. Rosvall & Bergstrom,PNAS, 2009

25. Network = Graph

26. Network analysis = Graph theory

27. Network analysis
= Graph theory+statistics+physics

28. What can we learn
from it?

29. Six degrees of separation
80-20 rule of social popularity

30. Grouping: Group similar people together
Ranking: Find the most influential people

31. Six degrees of separation

32. Six degrees of separation
Any person in the world needs only to take
at most six steps to reach any other person

33. How to measure how separated we
are?

34. Diameter
Longest shortest path among all pairs
How many steps a person has to take to
reach anyone

37. Average path length
Shortest path lengths averaged among all
possible pairs

38. The small-world network

43. Small-world network

44. Milgram’s experiment
Omaha & Wichita ->
Boston
64 out of 296
reached destination
Average path length
5.5

45. Watt’s Experiments
60,000 email users to
reach 18 targets in 13
countries
Dodds et al., Science, 2003

46. Back-of-the-envelope
calculation
50k
= 7,000,000,000

47. Back-of-the-envelope
calculation
50k
= 7,000,000,000
k = log50 (7,000,000,000) = 5.8

48. Erdos number
Mathematicians’ co-publishing network
Average path length – 4.65

49. Bacon number
Actors’ co-starring network
Average path length – 3.65

51. 1

52. 2
1

53. (some
mathematicians
and papers that
nobody cares
about)

54. 5
2

56. Be nice to the old lady slowly
crossing the street

57. 80-20 rule of social popularity

59. How to measure the popularity of the
nodes?

60. Degree distribution
The probability distribution of the number of
links of a node
P(deg(v)= k)

62. N=10000, p=0.02

63. Degree distribution
http://en.wikipedia.org/wiki/Erdos-Renyi_model

64. What does a real network look like?

65. Mahadevan et al., SIGCOMM, 2007

66. Newman, SIAM Review, 2003

67. Power-law distribution
P(k) ~ k-g

68. Theory vs Reality
H. Jeong et. al, Nature (2000)

69. Power-law distribution
Long-tail distribution: Nodes with extremely
large number of links have non-trivial
chance to appear

70. Power-law distribution
80-20 rule of social network: A minority of
nodes have a majority of links

72. What’s wrong with the random
network model?

73. Barabasi-Albert model
When a new node joins the network, it
connects to popular existing nodes

74. Barabasi-Albert model
When a new node joins the network, it
connects to popular existing nodes
The probability is proportional to the existing
node’s number of links

76. Scale-free network
Matthew Effect: Richer-get-richer
Links is the “wealth” in social network

77. Like wealth, social popularity follows
80-20 rule

78. Rank the nodes according to their
important

79. PageRank
Relative importance of nodes

80. PageRank
Probability of opening a page when surfing
the Internet

81. PageRank
Probability of arriving at this page from other
pages that link to it

82. PageRank
Probability of arriving at this page from other
pages that link to it, or randomly opening
this page

86. Group similar nodes together

88. Communities
Friends from middle school, college, and
work
How do we group them?

89. Guimera & Amaral, Nature, 2005

90. How to measure the tendency to
form communities?

91. Modularity
How well the network can be separated into
modules

92. For every module,

93. For every module, calculate the number of
links within the module

94. For every module, calculate the number of
links within the module, minus its
expectation

95. Compare to its expectation

96. Maximize modularity
NP hard
Simulated annealing: slow, accurate
Louvain method: greedy, fast, local-
minimum

99. Guimera et al., PNAS, 2005

102. Dynamics on network
SIR model in NetLogo

103. Multiplex network
Facebook, Twitter, LinkedIn

104. Radicchi & Arenas, Nature Physics, 2014

105. De Domenico et al., PNAS, 2014

106. How do we do it?

107. Python + Spark
networkx
matplotlib
pyspark

108. Co-purchase network
Who bought the same deals as you did?

109. Data
User 1, Deal A
User 1, Deal B
User 1, Deal C
User 2, Deal A
User 3, Deal B
…

110. 1 A
2 B
3 C
4 D

111. 1 A
2 B
3 C
4 D

112. 1 A
2 B
3 C
4 D

113. 1
2
3
4

114. 1
2
34

115. IPython notebook

117. Diameter: 6
Average path length: 2.57

119. Largest groups
Group 1
- 395 females, 201 males
- Average age: 42.4
Group 2
- 228 females, 83 males
- Average age: 38.9
Group 3
- 51 females, 27 males
- Average age: 34.1

120. Group 1 vs 2: p-value = 0.001
Group 1 vs 3: p-value < 0.001
Group 2 vs 3: p-value < 0.001

122. IPython notebook
Examples of networks:
https://github.com/zengxiaohanzxh/network
s-ipython.git
Groupon example:
git@github.groupondev.com:zengxiaohanzx
h/networks.git

123. Xiaohan Zeng <xzeng@groupon.com>
Quantum Lead, 6th floor near Fishbowl