1. Social Networks Analysis
Week 2

2. sna measurements Relational Data From Social Data to Relational Data
Nodes & Ties
Dyad
Triad
Subgroup
Group
Degree
Centrality and Power
Density
Path Length & Neighborhoods
Small World
Clustering Coefficient
Structural Hole
Clique

3. Node/Actor
“discrete individual, corporate, or collective social units” (Wasserman/Faust 2008:17)
Examples: people in a group, departments within in a corporation, public service agency in a city, nation-states in the world system
Does not imply that they have volition or the ability to “act”

4. Size
Number of Nodes

5. Ties/Links
Different types of ties: family, friend, personal / professional, ego-perceived / alter-perceived / mutual
Directed (Flickr) / Undirected (Facebook)
Strong & Weak ties
Amount of time, emotional intensity, intimacy and reciprocal services

6. Dyad a tie between two actors
“consists of a pair of actors and the (possible) tie(s) between them” (Wasserman/Faust 2008:18)
Shows “properties of pairwise relationships, such as whether ties are reciprocated or not, or whether specific types of multiple relationships tend to occur together” (Wasserman/Faust 2008:18)

7. Triad
“Triples of actors and associated ties” (Wasserman/Faust 2008:19)
“a subset of three actors and the (possible) tie(s) among them” (Wasserman/Faust 2008:19)
Triadic analyses focus on the fact whether the triad is
Transitive : if actor i “likes” actor j, and actor j in turn “likes” actor k, then actor i will also “like” actor k
Balanced: if actors i and j like each other, then i and j should be similar in their evaluation of a third actor, k, and i and j dislike each other, then they should differ in their evaluation of third actor, k

8. Subgroup
Subgroup of actors is defined “as any subset of actors, and all ties among them” (Wasserman/Faust 2008:19)

9. Group
“is the collection of all actors on which ties are to be measured” (Wasserman/Faust 2008:19)
Actors in a group “belong together in a more or less bounded set (…) consists of a finite set of individuals on which network measurements are made” (Wasserman/Faust 2008:19)
“The restriction to a finite set or sets of actors is an analytic requirement. Though one could conceive of ties extending among actors in a nearly infinite group of acts, one would have great difficulty analyzing data such a network. Modeling finite groups presents some of the more problematic issues in network analysis, including the specification of network boundaries, sampling, and the definition of group. Network sampling and boundary specification are important issues.” (Wasserman/Faust 2008:19f.)
“however, in research applications we are usually forced to look at finite collections of actors and ties between them.” (Wasserman/Faust 2008:20)

10. Degree Number of links that a node has
It corresponds to the local centrality in social network analysis
It measures how important is a node with respect to its nearest neighbors
Directed Graph
Indegree & Outdegree

11. What is the size of the graph
What is the In-Degree & Out-Degree of Node 5 ?
What is the In-Degree & Out-Degree of Node 4 with weight ?

12. Path Length
AB, AE, and BE have path length of 1 (1 line connects each pair of points)
A and C are connected through B and have a path length of 2 (2 lines)
there are no isolated points
every point can reach every other point within 2 steps

13. Path AD has a path length of 1
the walk ABCAD is not a path (passes through A twice!)
ABCD has a path length of 3
A and D are connected by 3 paths
AD – length 1
ACD – length 2
ABCD – length 3
the distance between A and D is equal to the shortest path

14. Path
directed graphs are similar except for the possible asymmetry of the relationship
degree has two separate components:
indegree: total numbers of alters related to ego; A=1, B=2, C=1
outdegree: total numbers of points ego relates to; A=1 , B=1 , C=2
paths: CAB is a path, CBA is not a path!

15. What is the path length from node 1 to node 9
Shortest path

16. Centrality & Power

17. Network & Power
Who has more power

18. Centrality
Degree, Betweenness, Closeness, Eigenvalue

19. Centrality in Social Networks : Degree
The most intuitive notion of centrality focuses on degree: The actor with the most ties is the most important:

21. Centrality in Social Networks : Degree

29. The closeness of node 4 in this graph
The betweeness of node 5 in this graph

30. Graph Density describes the general level of contectedness in a graph
graph is complete if all points are adjacent to each other
the more points that are connected, the greater the density
there are two components for density
inclusiveness: number of points that are included in the graph because they are connected
total degree: sum of degree of all the points

31. Graph Density

32. Graph Density Example

33. The density of this graph?

34. Clustering Friends of friends are likely to be friends
Clustering coefficient, C (0 <= C<= 1)
Density of triangles in the network
Density of links that exist between one’s friends

35. Cluster Coefficient

36. The clustering coefficient of node 1, 2, 3, 4, 5, 6

37. Structural Hole

38. Clique Measurement Clique Complete subgraph Maximum clique {1,2,5}
Maximal cliques
{2,3}, {3,4}, {4,5},{4,6}
K-clique
Clique of size k

39. Please find all the 3-cliques in this graph