Social Network Analysis: What It Is, Why We Should Care, and What We Can Learn From It
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Transcript of Social Network Analysis: What It Is, Why We Should Care, and What We Can Learn From It
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Social Network AnalysisWhat it is, what we can learn from it, and how we can do it
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Backstrom & Kleinberg, 2014
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Predict your partner
1.3m users in a relationship, 379m people, 8.6b connections
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Predict your partner
1.3m users, 379m people, 8.6b connections
Accuracy: 60%
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Andris et al., PLoS ONE, 2015
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What is it?
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Social networks connect people
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Social network
A social structure that represents the relationships between people
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Social network
A graph model that represents the dyadic relationships between people
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Nodes and Edges
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Nodes and Edges
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Nodes and Edges
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Nodes and Edges
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Network
A graph model that represents the dyadic relationships between entities
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Ahn et al.,Sci. Rep., 2011
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Weighted network
Links can have a weight
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Directed network
Links can be directed
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Rosvall & Bergstrom,PNAS, 2009
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Network = Graph
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Network analysis = Graph theory
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Network analysis= Graph
theory+statistics+physics
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What can we learn from it?
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Six degrees of separation
80-20 rule of social popularity
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Grouping: Group similar people together
Ranking: Find the most influential people
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Six degrees of separation
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Six degrees of separationAny person in the world needs only to take at most six steps to reach any other person
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How to measure how separated we are?
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Diameter
Longest shortest path among all pairs
How many steps a person has to take to reach anyone
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Average path length
Shortest path lengths averaged among all possible pairs
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The small-world network
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Small-world network
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Milgram’s experiment
Omaha & Wichita -> Boston
64 out of 296 reached destination
Average path length 5.5
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Watt’s Experiments
60,000 email users to reach 18 targets in 13 countries
Dodds et al., Science, 2003
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Back-of-the-envelope calculation
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Back-of-the-envelope calculation
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Erdos number
Mathematicians’ co-publishing network
Average path length – 4.65
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Bacon number
Actors’ co-starring network
Average path length – 3.65
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1
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2
1
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(some mathematicians and papers thatnobody cares
about)
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5
2
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Be nice to the old lady slowly crossing the street
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80-20 rule of social popularity
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How to measure the popularity of the nodes?
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Degree distribution
The probability distribution of the number of links of a node
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N=10000, p=0.02
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Degree distribution
http://en.wikipedia.org/wiki/Erdos-Renyi_model
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What does a real network look like?
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Mahadevan et al., SIGCOMM, 2007
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Newman, SIAM Review, 2003
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Power-law distribution
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Theory vs Reality
H. Jeong et. al, Nature (2000)
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Power-law distribution
Long-tail distribution: Nodes with extremely large number of links have non-trivial chance to appear
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Power-law distribution
80-20 rule of social network: A minority of nodes have a majority of links
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What’s wrong with the random network model?
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Barabasi-Albert model
When a new node joins the network, it connects to popular existing nodes
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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
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Scale-free network
Matthew Effect: Richer-get-richer
Links is the “wealth” in social network
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Like wealth, social popularity follows 80-20 rule
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Rank the nodes according to their important
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PageRank
Relative importance of nodes
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PageRank
Probability of opening a page when surfing the Internet
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PageRank
Probability of arriving at this page from other pages that link to it
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PageRank
Probability of arriving at this page from other pages that link to it, or randomly opening this page
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Group similar nodes together
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Communities
Friends from middle school, college, and work
How do we group them?
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Guimera & Amaral, Nature, 2005
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How to measure the tendency to form communities?
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Modularity
How well the network can be separated into modules
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For every module,
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For every module, calculate the number of links within the module
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For every module, calculate the number of links within the module, minus its expectation
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Compare to its expectation
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Maximize modularity
NP hard
Simulated annealing: slow, accurate
Louvain method: greedy, fast, local-minimum
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Guimera et al., PNAS, 2005
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Dynamics on network
SIR model in NetLogo
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Multiplex network
Facebook, Twitter, LinkedIn
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Radicchi & Arenas, Nature Physics, 2014
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De Domenico et al., PNAS, 2014
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How do we do it?
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Python + Spark
networkxmatplotlibpyspark
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Co-purchase network
Who bought the same deals as you did?
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Data
User 1, Deal AUser 1, Deal BUser 1, Deal CUser 2, Deal AUser 3, Deal B…
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1 A
2 B
3 C
4 D
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1 A
2 B
3 C
4 D
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1 A
2 B
3 C
4 D
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1
2
3
4
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1
2
34
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IPython notebook
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Diameter: 6
Average path length: 2.57
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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
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Group 1 vs 2: p-value = 0.001Group 1 vs 3: p-value < 0.001Group 2 vs 3: p-value < 0.001
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IPython notebook
Examples of networks:https://github.com/zengxiaohanzxh/networks-ipython.git
Groupon example: [email protected]:zengxiaohanzxh/networks.git