1. Network analysis basic

2. • in-degree: how many directed edges (arcs)
are incident on a node
• out-degree: how may directed edges
originate at a node
• Degree sequence: [4, 4, 3, 7, …]
Node properties

3. Generated properties of node
• Clustering coefficient: how your neighbors
connected together
• ego-density: density of the surrounding net
UCINET: Network>Ego-networks>egonet basic measures

4. • Directed or undirected
• Weight, ranking, ...
• Type, negative or positive, ...
• Assigned-properties depending on
calculating network itself, e.g., betweenness
Edge properties

5. Network Properties
• Degree distribution: Frequency of degree
sequences
• Size: number of nodes (n)
• Density: real relations divided by the maximum
possible relations
• Diameter: the length of the longest path
• Average degree of separation:Average length of all
possible shorted path
UCINET: Network>Cohesion>Density

6. Mode of network
• One-mode network
‣ Friendship
‣ Collaboration e.g., User-paper represented by 2-mode network
• Two-mode network—bipartite network
‣ User-borrowed book, co-bought
‣ Affiliation network— e.g., Member-Guild, Employee-Company

7. Resolved by co-occurrence-ship

8. Network analysis basic

9. • Degree
How many resource do you have?
• Closeness
How far apart are you from others?
• Betweenness
How important are you for bridging
sub-communities?
• Centralization
How balanced are actors’ centrality?
Centrality
Individual
level
Global
level

10. • Density
How does the network tied together?
• Separation, Diameter
How far apart are you and your friends?
• Cluster Coefficient
How do your neighbors be connected?
Individual
level
Global
level

11. Visualization through analysis process
1. Take a look
2. Analyze and find significant features such as sub-
components or special positions
3. Draw the network according to the result of
analysis
4. Color by the node features (e.g., sex, position, ...)
and create hypothesis
5. Verify the hypothesis

12. • Ego-network Analysis
-
-
• Partial Network Analysis
- One, two or three steps network two steps network
- Boundary or sub-cluster of network
• Whole Network Analysis
- /
Motif
-
Levels of network analysis

13. • Data is recorded with a clear natural-occurring
boundary and nodes in a boundary form a finite
set.
• What should be a possible boundary?
‣ A fixed location or room, specified time or day, a finite contact
tracing, a formal group in an organization, a family.
‣ The boundary is known or decided firstly, a priori, to be a
network.
Policy of recording data

14. • No sampling and tend to include all of the actors
in some population(s).
• Because network methods focus on relations
among actors, actors cannot be sampled
independently to be included as observations.
Policy of recording data (2)

15. • positivity A Priori
metaphysics
-
• -
• -
-
Butts, Carter T. "Revisiting the foundations of network analysis." Science325.5939 (2009): 414-416.

16. • Closed Complete
- finite
set
-
• Singularity
-
• Consistency
-
Butts, Carter T. "Revisiting the foundations of network analysis." Science325.5939 (2009): 414-416.

17. • Different relation sampling policy will cause
different results—Threshold effects on network
properties
• Threshold
Threshold
• Threshold 0
Connectedness
Betweenness
• Threshold Betweenness
Degree Betweenness
• facebook
10
Application

18. • Full network data is necessary to properly define and measure
many of the structural concepts of network analysis (e.g.
between-ness), however, very expensive.
• Snowball methods begin with a focal actor or set of actors until
no new actors are identified, or until we decide to stop.
- Useful to track down “special” population such as business contact networks, community
elites, deviant sub-cultures, avid stamp collectors, and kinship networks.
- The snowball method may tend to overstate the "connectedness" and "solidarity" of
populations of actors.
- There is no guaranteed way of finding all of the connected individuals in the population.
- How to select the first node (initial problem of sampling)?
- Incomplete problem of the snowball methods can be solved by use of multiple initial nodes.
Methods of sampling ties

19. Visualization

20. X Crossed-edges
X Uninformed-edge
length
X Overlapped
nodes and edges

24. A B C D E F G H I J
A 0 1 1 1 0 1 0 0 0 0
B 1 0 0 1 1 0 1 0 0 0
C 1 0 0 1 0 1 0 0 0 0
D 1 1 1 0 1 1 1 0 0 0
E 0 1 0 1 0 0 1 0 0 0
F 1 0 1 1 0 0 1 1 0 0
G 0 1 0 1 1 1 0 1 0 0
H 0 0 0 0 0 1 1 0 1 0
I 0 0 0 0 0 0 0 1 0 1
J 0 0 0 0 0 0 0 0 1 0
Adjacent matrix
degree of B
Symmetric
M(1,4)=1, M(1,5)=0

25. Homans(1951) Metrics representation and manipulation
A B C D E F G H
A 1 1 1 1 1
B 1 1 1
C 1 1 1 1
D 1 1 1
E 1 1 1
F 1 1 1
G 1 1 1
H 1 1 1 1
D E C H A B F G
D 1 1 1
E 1 1 1
C 1 1 1 1
H 1 1 1 1
A 1 1 1 1 1
B 1 1 1
F 1 1 1
G 1 1 1