1. Structural Holes & Weak Ties
Overview
Granovetter: Strength of Weak Ties
What are ‘weak ties’?
why are they ‘strong’?
Burt: Structural Holes
What are they?
What do they do?
How do they work?
“Good Ideas”
Methods & Measures:
1) Moving data around
SAS Data steps
2) Calculating Ego-Network Measures
From Ego-network modules
From Global Networks

2. Local Density, Global Fragmentation
Structural Holes & Weak Ties
Granovetter argues that, under many circumstances, strong ties are less useful than weak ties. Why?
Redundancy
Local Density, Global Fragmentation

3. What are the implications?
Structural Holes & Weak Ties
The Strength of Weak Ties
What are the implications?
For individuals?
For Communities?

4. What is (for Burt) Social Capital? Relationships with other players
Structural Holes & Weak Ties
Structural Holes
Burt. Structural Holes
Similar idea to SWT: Your ties matter because of who your connects are not connected to.
What is (for Burt) Social Capital?
Relationships with other players
Why does it matter?
“Social capital is as important as competition is imperfect and investment capital is abundant.”

5. Structural Holes & Weak Ties
A structural Hole is a buffer: a space between the people you are connected to.
2 ways:
Cohesion
Structural Equivalence

6. Maximize the number of non-redundant contacts Effectiveness
Structural Holes & Weak Ties
Structural Holes
Efficiency
Maximize the number of non-redundant contacts
Effectiveness
Draw your primary contacts from different social worlds

7. Structural Holes & Weak Ties Structural Holes
Maximum
Efficiency
Decreasing Efficiency
Number of Non-Redundant Contacts
Increasing Efficiency
Minimum
Efficiency
Number of Contacts

8. Difference between SWT & SH:
Structural Holes & Weak Ties
Structural Holes
Difference between SWT & SH:
Burt’s claim is that he focuses directly on the causal agent active in Granovetter.
(but note the footnote in “good ideas,” where he says the effect is not causal).

9. Structural Holes & Weak Ties Good Ideas
The hypothesis is that those who broker different groups are exposed to different ideas and thus more likely to have a good idea.
Uses data on discussions among managers in a large electronics firm.

10. Structural Holes & Weak Ties
Good Ideas
Burt’s idea discussion network

11. Structural Holes & Weak Ties
Good Ideas
Burt’s idea discussion network

12. Figure 3: Core network in the supply chain
Structural Holes & Weak Ties
Good Ideas
Figure 3: Core network in the supply chain
With headquarters

13. Figure 3: Core network in the supply chain
Structural Holes & Weak Ties
Good Ideas
Figure 3: Core network in the supply chain
Without headquarters

14. Structural Holes & Weak Ties Good Ideas
The results show a strong effect of network constraint on salary, evaluation and promotion, independent of the job/age characteristics related to human capital explanations.

15. Structural Holes & Weak Ties Good Ideas
The results show a strong effect of network constraint on salary, evaluation and promotion, independent of the job/age characteristics related to human capital explanations.

16. Structural Holes & Weak Ties
Good Ideas

17. Calculating the measures
Structural Holes & Weak Ties
Calculations
Calculating the measures
Burt discusses 4 related aspects of a network:
1) Effective Size
2) Efficiency
3) Constraint
4) Hierarchy

18. Effective size = Size - Redundancy
Structural Holes & Weak Ties
Calculations
Effective Size
Conceptually the effective size is the number of people ego is connected to, minus the redundancy in the network, that is, it reduces to the non-redundant elements of the network.
Effective size = Size - Redundancy

19. Burt’s measures for effective size is:
Structural Holes & Weak Ties
Calculations
Effective Size
Burt’s measures for effective size is:
Where j indexes all of the people that ego i has contact with, and q is every third person other than i or j.
The quantity (piqmjq) inside the brackets is the level of redundancy between ego and a particular alter, j.

20. Piq is the proportion of actor i’s relations that are spent with q.
Structural Holes & Weak Ties
Calculations
Effective Size:
Piq is the proportion of actor i’s relations that are spent with q. 3 2
Adjacency P 1 5 4

21. Structural Holes & Weak Ties
Calculations
Effective Size:
mjq is the marginal strength of contact j’s relation with contact q. Which is j’s interaction with q divided by j’s strongest interaction with anyone. For a binary network, the strongest link is always 1 and thus mjq reduces to 0 or 1 (whether j is connected to q or not - that is, the adjacency matrix).
The sum of the product piqmjq measures the portion of i’s relation with j that is redundant to i’s relation with other primary contacts.

22. Effective Size: 3 2 1 5 4 Sum=1, so Effective size = 4-1 = 3.
Structural Holes & Weak Ties
Calculations
Effective Size: 3 2
Working with 1 as ego, we get the following redundancy levels: 1 P
PM1jq 5 4
Sum=1, so
Effective size = 4-1 = 3.

23. Structural Holes & Weak Ties
Calculations
Effective Size: 3 2
When you work it out, redundancy reduces to the average degree, not counting ties with ego of ego’s alters. 1 5 4
Node Degree
2 1
Mean: 4/4 = 1

24. Since the average degree is simply another way
Structural Holes & Weak Ties
Calculations
Effective Size: 3 2
Since the average degree is simply another way
to say density, we can calculate redundancy as:
2t/n
where t is the number of ties (not counting ties to ego) and n is the number of people in the network (not counting ego).
Meaning that effective size =
n - 2t/n 1 5 4

25. Efficiency is the effective size divided by the observed size.
Structural Holes & Weak Ties
Calculations
Efficiency is the effective size divided by the observed size. 3 2
Effective
Node Size Size: Efficiency 1 5 4

26. Structural Holes & Weak Ties
Calculations
Constraint
Conceptually, constraint refers to how much room you have to negotiate or exploit potential structural holes in your network. 3 2 1 5 4
“..opportunities are constrained to the extent that (a) another of your contacts q, in whom you have invested a large portion of your network time and energy, has (b) invested heavily in a relationship with contact j.” (p.54)

27. Constraint 3 2 1 5 4 Structural Holes & Weak Ties Calculations P

28. q i j Constraint pij piq pqj
Structural Holes & Weak Ties
Calculations
Constraint q i j
pij
piq
pqj
Cij = Direct investment (Pij) + Indirect investment

29. Structural Holes & Weak Ties
Calculations 3 2
Constraint 1 5 4
Given the p matrix, you can get indirect constraint (piqpqj) with the 2-step path distance.
P*P P

30. Total constraint between any two people then is:
Structural Holes & Weak Ties
Calculations
Constraint
Total constraint between any two people then is:
C = (P + P2)##2
Where P is the normalized adjacency matrix, and ## means to square the elements of the matrix.

31. Constraint Structural Holes & Weak Ties Calculations P+P2 Cij C

32. Structural Holes & Weak Ties
Calculations
Hierarchy
Conceptually, hierarchy (for Burt) is really the extent to which constraint is concentrated in a single actor. It is calculated as:

33. Hierarchy 3 2 1 5 4 H=.514 Structural Holes & Weak Ties Calculations 5 4
H=.514

34. Playing with data: Getting information from one program to another
If our data are in one format (SAS, for example) how do we get it into a program like PAJEK or UCINET?
1) Type it in by hand.
Too slow, error prone, impossible for very
large networks
2) Write a program that moves data around for you
automatically
SPAN contains programs that write to:
PAJEK
UCINET
NEGOPY
STRUCTURE

35. Playing with data: Using SAS to move data.
Basic Elements:
SAS is a language:
Data Steps = Nouns
Procedures = Verbs
Data needs:
Creation / Read
Organization
Transformation
Manipulation
Procedures:
Summarize
Analyze
Communicate
Manipulate
Back-up:
1) How does SAS store & move data?
2) How do you store & use programs over again?

36. SAS
The procedure we have been using is IML or the
Interactive Matrix Language.

37. Data
Libraries: Links to where data are stored
Datasets: the actual data
You refer to a data set by a two-level name:
library.data