Exploratory Social Network Analysis Chapter 10: Ranking

1. Exploratory Social Network Analysis
Ranking

2. Prestige
Continuous Scale
For Each Actor
Overall Discrete Class  Social Strata  Social Class
Working, Middle, Upper
Ranking
Social Ranking
Formal e.g. Army
Informal
Opinions & Behavior of People toward each other:
Respect & Deference Vs. Disrespect & Dominance  Sociometry
Comparison: Deviation of Society from the Official Communication Structure.

3. Rephrase Balance Theory
• Symmetric Relationships: DYAD
• Love
• Hate
• Reciprocation!
• Mutual  Same Strata Same Rank
• Null  Different Strata Same Rank
• Asym  Strata Ranking

4. Triadic Analysis
M-A-N Number
M Mutual Dyads
A Rank Dyads
N Null Dyads
[letter] Asymmetric Choices Direction in Same Digits
Down, Up, Cyclic, Transitive

6. Stratum Membership
Ties within Clusters Ties between Ranks Permitted Triads
Balance
Symmetric ties
within a cluster, no
ties between
clusters max. two
clusters
None
Clusterability
Idem no restriction
on the number of
clusters
Idem
Rank Idem
Asymmetric ties from
each vertex to all
vertices on higher
ranks
Transitive Idem
Null ties may occur
between ranks
Hierarchical
Asymmetric ties
within a cluster
allowed provided
that they are
acyclic
Idem +120C, 210
No Balance
Theoretic Model
(Forbidden)
021C, 111D, 111U, 030C, 201
+ sign indicates that all triads in previous rows are also permitted

7. Micro 2 Macro Scope  Triadic Census

8. Acyclic Network
GOBeyond Dyads & Triads  Strong Component
Strong Component Form Mutual Love!
Each Node in Strong Component has Directed to Others
Symmetrically
Ranking in Components
Shrink Strong Components
Acyclic Network Asymmetric Love!

9. Symmetric-Acyclic
In Strong Component
Each Step of a Path
Mutual Dyad.

10. Triadic Analysis
Info > Network > Triadic Census
Acyclic Network
Net > Components > Strong
Operations > Shrink Network > Partition
Symmetric-Acyclic Decomposition
Net > Hierarchical Decomposition > Symmetric-Acyclic.
Find the original network vertices in the resulting symmetric acyclic clusters.
Partitions > Expand