This document provides an overview of social network analysis (SNA). It defines key SNA concepts like nodes, edges, networks and visualization of networks using graphs. It discusses different types of networks and models for network growth. It also covers centrality measures to determine node importance, methods for identifying communities, and software tools like Netlogo and Gephi for SNA. Examples of visualizing online student interaction networks in Moodle and Google+ using these concepts and tools are also presented.

1. Social Network
Analysis
Jutta Pauschenwein
ZML-Innovative Lernszenarien
FH JOANNEUM

2. 2

3. COS16 – week 1
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4. 4
Coursera MOOC: 8 weeks, autumn 2014

5. Why SNA?
I want to understand data
through visualization
Woche 1 im SNA-MOOC
5

6. Definitions
• network: set of connected nodes (social: connection via relation-ship)
• nodes: nodes, actors, sites, vertices
• connections: edges, ties, relations
• visualize networks by graphs
4 communities
MOOC, week1
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7. Questions
structure of the network
• Are the nodes connected? How far
are they from each other? Are some
nodes more important than others?
Are there communities in the
network?
types if networks
• randomly generated connections,
network with preferences, small world
networks (most nodes are not
neighbours of one another, but the
neighbours of any give node are
likely to be neighbours of each other)
small-world-network, MOOC week 5
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8. • connections are directed / not directed
• weighted connection
• a node with several degrees
A communciates with B
A communcates with B and B with A
A communciated with B 4x
Connections
8
Communication of students
in google+ 4 days

9. Erdős-Rényi Graph
• simple network with fixed number of nodes
• assumption 1: nodes connect randomly
• assumption 2: network is not directed
• assumption 3: N nodes, M connections, p probability that two nodes connect
• in this network type there appear no hubs, but the „giant component“
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10. Reale networks grow
Expansion of the Erdős-Rényi approach
• growing networks, for example WWW, citation networks
Models
• random preferential: new nodes prefer to connect to already
well connected nodes
• introduction model: nodes were presented to each other
• static geographic model: nodes connect to the neighbours of
the nodes they are connected with
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11. Barabasi-Albert model
• there’s a probabilty that each node connects with
another node in dependence of its degree
• There’s an initial configuration and then the process
of connecting starts with an
• each new node has a certain probability of m to
connect to the network
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preferential
model
netlogo

13. in the preferential model you get hubs because „old“ nodes have more time to connect
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14. Centrality
What importance has a node in the network?
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degree centrality
the node is an active player in the network, it is well
connected

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betweeness centrality
„broker“ - all communication uses this node
If the node doesn’t work, the connection in the network fails.

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closeness
Closeness is the distance of one node to all the other nodes - it is enough
to be near a hub

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eigenvector centrality
The importance of a node increases with the importance of its neighbours.

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Which node has a small degree but a
high betweeness?
Or reversed?

20. Find communities
How to define a community / substructur in a network?
• There are many connections within a community.
• The other nodes in a community are only at a distance of some hops.
• Nodes in one community are strongly connected.
It’s difficult to find communities if you don’t know the number of communities - there are
large and small communities.
Parameters:
• minimum cut: number of communities
• hierarchical clustering: clustering based on certain characteristics
• betweennes clustering: connections with the highest betweennes are removed
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Problem: when do you stop to remove connections?
=> Modularity - comparison, how many connections are within and outside of the community
In a network the number of connections within a community increases and the number of connections to
nodes outside of the community decreases
http://spark-public.s3.amazonaws.com/sna/other/guess/betweennessclust.html

22. 3 communities of my facebook friends (2014)

23. Software
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Netlogo
• programmable modeling environment for simulating natural and social
• phenomena
• Free, open source - cross-platform: runs on Mac, Windows, Linux, et al
• https://ccl.northwestern.edu/netlogo
Gephi
• interactive visualization and exploration platform for networks and
complex
• systems, dynamic and hierarchical graphs.
• Runs on Windows, Linux and Mac OS X. Gephi is open-source and free
• http://gephi.github.io/

24. Visualization of online
groups: data
master program
WS 14/15
4 days in Nov. 2014
Google+
collection of data by hand

25. how individual persons and the
group interact
one person is more active than
the teacher

26. Size of nodes according to degree
Color according to betweenness
master program WS 14/15
3 weeks of online socialisation
Interaction in Moodle

27. Same group as before
Interaction during the whole semester

28. Same group
4 communities

29. training course14/15
size of nodes according to degree
color according to betweeness
2 communities

30. Conclusion
• SNA is complex, has a high potential
• I get new insights in my groups - but I don’t understand it entirely until
now - there’s a lot of theory behind
• I use it to get a quick insight how a group is performing - in my role as
convener/moderator