1. A Gentle Introduction to Social Network Analysis
From a Sociologist’s Perspective
Reuben (Jack) Thomas
April 2017

2. The Structure of Relationships
Relationships as the unit of analysis, but not as isolated units: their interconnection, their collective structure

3. Ties and Nodes Ties (Edges, Arcs) indicate relationships
Nodes (Vertices) indicate social entities that form the relationships

4. Ties can be… Nodes can be… Exchanges & Transactions Alliances
Friendships
Enemies
Sexual Encounters
Murders
Joke Telling
Collaborations
Co-sponsorship
Co-attendance
Lending a hand
People
Places
Boats
Organizations
Social Movements
Works of Art
Events
Dogs
Countries
Schools of Thought
Memes

5. Ties can vary by… Strength (Valence) – binary ties vs weighted ties
Multiplex: multiple types\roles\exchanges\etc in the relationship (vs Simplex)
Directed vs Undirected
Other variables about the relationship

6. Network Data can be
Complete (Sociocentric): a sampling of ties within a predefined group
Egocentric: a sampling of ties from unconnected nodes. (e.g. survey data from a national sample)

7. Network Data: Arc List Ego Alter Tie Strength Bob Maria 1 Bob Weiwei 1
Maria Weiwei 1
Weiwei Maria 1

8. Network Data: Adjacency Matrix
Bob Maria Weiwei
Bob
Maria
Weiwei

9. Network Data: Affiliation Matrix
Karate Spanish Swim
Bob
Maria
Weiwei

10. Multi-Mode Networks
People and Groups Corporations and Governments Scientists and Papers and Journals and Disciplines Ships and Captains and Ports

12. Social Network Visualization

13. Density What proportion of dyads are connected?
Number of Ties / Number of Possible Ties
Density = 2(Edges) / Nodes(Nodes-1)

14. Network Distances Shortest Paths (Geodesics)
The Diameter of a network is the length of its longest Geodesic
Reachability or Connectedness:
Can every node reach every other node?
All geodesics are1 in perfectly dense networks

15. Six Degrees of Separation

16. Centrality
How central is a node to the network, or how peripheral?

17. Degree-Centrality
Having a lot of connections This is just the number of ties a node has In-degree vs Out- degree in directed networks

18. Eigenvector Centrality
Having a lot of connections to people who have a lot of connections to people who... (recursive)
Google’s PageRank is based on this idea

19. Closeness Centrality
Being close to everyone in the network. The Farness of a node is the average distance to all other nodes in the network The Closeness of a node is the inverse of its Farness

20. Betweenness Centrality
Being between a lot of people in the network. Being on many geodesics. The Betweenness of a node is the proportion of all the geodesics in the network that the node is a part of.

21. Clustering & Transitivity
“My friends are friends”
Transitivity
Triangle completion rate
The Clustering Coefficient:
Actual links between alters / Possible links between alters
Actual triangles / Possible triangles

22. Lack of diamond-clustering can create spanning trees in hetero-sexual networks

23. Community Structure & Cohesion
Cliques, the Idea: sub-sets of the network in which nodes are more closely\strongly tied to each other. Formal definitions vary. A Maximal Clique is as big as possible while remaining perfectly dense. Less strict Clique definitions can be tricky (N-Cliques, N-Clans)

24. Cliques, Clans & Cores
N-Cliques: All members must be mutually reachable at distance N. N-Clans: …but only through other members K-Cores: subgraphs within which all nodes have at least K ties (e.g. in a 4-core all nodes have at least 4 ties within it) Also see K-plexes, F-Groups, etc.

25. K-Connectivity
The minimum number of actors you need to remove to break the network in two. You can talk about K-edge-connected vs K-vertex-connected.
K-cutsets: the cliques formed by cutting K nodes/edges out

26. Betweenness Partitioning
Remove edges that are the most “between” to reveal nested networks

27. Segregation \ Assortativity \ Homophily
Are ties disproportionately between similar nodes?
Can refer to any characteristic, not just groups: age, centrality, GPA, GDP, delinquency, height, hygiene, etc.

29. Equivalence Structural Equivalence Automorphic Equivalence
same ties to same nodes
Automorphic Equivalence
indistinguishable structural position (but maybe not same alters)
Regular Equivalence
connected to equivalent alters (but maybe not same number of alters)

30. Statistical Models for Network Data
Approaches vary by discipline, a lot
in Sociology, ERGMS and SENIA are popular now, QAP models used to be

31. Quadratic Assignment Procedure (QAP) Regression
Or, “Why can’t I just use dyadic data in a regular regression?” Answer: Auto-correlation, big time Solution: randomly switch who is tied to whom in the data many many times, re-estimating the model each time, to create an unbiased distribution of possible samples for calculating the standard errors. Appropriate when your cases are dyads within a network, and your dependent variable is information about the dyad.

32. Exponential Random Graph Models (ERGMs)
Or, “Can’t we just run a logit on this?” The goal is to calculate the odds of a tie, controlling for aspects of network structure and dyadic variables. (earlier versions were called p* models)

33. Dynamic Networks
An awful lot of SNA has treated networks as static things, but they rarely are.
The cutting edge of SNA is all about modeling dynamic change in networks.

34. SIENA Simulation Investigation for Empirical Network Analysis
Similar to ERGMs, but specifically developed for dynamic network data.
I don’t really know it, ask Dan Ragan and Brian Soller.

35. Free Software!
NodeXL: The easiest visualization tool I’ve used, but 1) it only works with Microsoft Excel in Windows, and 2) it is no longer free for advanced features. Also calculates some metrics.
Gephi: Another nice visualization tool, works with Macs, Linux and Windows alike, and its open source.
Pajek: Once the favorite visualization tool in SNA, and still popular
SoNIA: a visualization software package for dynamic data (network movies!)

36. Not Free but Useful
UCINET: relatively easy to use and versatile SNA package, free trial

37. Free but Advanced R Packages:
statnet: for Exponential Random Graphs (ERGMs), by UW-Seattle
igraph: nice visualization tools, also in Python and C\C++
sna: a package of various SNA tools developed by Carter Butts at UC-Irvine
RSiena: just like it sounds, run SIENA models in R

38. Good Intro to SNA Books John Scott’s Social Network Analysis
David Easley & Jon Kleinberg’s Networks, Crowds, and Markets: Reasoning About a Highly Connected World
Duncan Watts’s Six Degrees: The Science of a Connected Age
Stanley Wasserman & Katherine Faust’s Social Network Analysis: Methods and Applications (this is more of a reference book)
(find these slides on my website: