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

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

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

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.”

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

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

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

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).

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.

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

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

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

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

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.

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.

Structural Holes & Weak Ties Good Ideas

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

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

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.

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 1 2 3 4 5 1 0 1 1 1 1 2 1 0 0 0 1 3 1 0 0 0 0 4 1 0 0 0 1 5 1 1 0 1 0 P 1 2 3 4 5 1 .00 .25 .25 .25 .25 2 .50 .00 .00 .00 .50 3 1.0 .00 .00 .00 .00 4 .50 .00 .00 .00 .50 5 .33 .33 .00 .33 .00 1 5 4

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.

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 1 2 3 4 5 1 .00 .25 .25 .25 .25 2 .50 .00 .00 .00 .50 3 1.0 .00 .00 .00 .00 4 .50 .00 .00 .00 .50 5 .33 .33 .00 .33 .00 PM1jq 1 2 3 4 5 1 --- --- --- --- --- 2 --- .00 .00 .00 .25 3 --- .00 .00 .00 .00 4 --- .00 .00 .00 .25 5 --- .25 .00 .25 .00 5 4 Sum=1, so Effective size = 4-1 = 3.

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 3 0 4 1 5 2 Mean: 4/4 = 1

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

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 4 3 .75 2 2 1 .5 3 1 1 1.0 4 2 1 .5 5 3 1.67 .55 1 5 4

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)

Constraint 3 2 1 5 4 Structural Holes & Weak Ties Calculations P 1 2 3 4 5 1 .00 .25 .25 .25 .25 2 .50 .00 .00 .00 .50 3 1.0 .00 .00 .00 .00 4 .50 .00 .00 .00 .50 5 .33 .33 .00 .33 .00

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

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 1 2 3 4 5 1 ... .083 .000 .083 .250 2 .165 ... .125 .290 .125 3 .000 .250 ... .250 .250 4 .165 .290 .125 ... .125 5 .330 .083 .083 .083 ... P 1 2 3 4 5 1 .00 .25 .25 .25 .25 2 .50 .00 .00 .00 .50 3 1.0 .00 .00 .00 .00 4 .50 .00 .00 .00 .50 5 .33 .33 .00 .33 .00

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.

Constraint Structural Holes & Weak Ties Calculations P+P2 Cij C .00 .33 .25 .33 .50 .00 .11 .06 .11 .25 .53 .67 .00 .13 .29 .63 .44 .00 .02 .08 .39 1.0 .25 .00 .25 .25 1.0 .06 .00 .06 .06 .67 .29 .13 .00 .63 .44 .08 .02 .00 .39 .66 .41 .08 .41 .00 .44 .17 .01 .17 .00

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:

Hierarchy 3 2 1 5 4 H=.514 Structural Holes & Weak Ties Calculations .83 .46 .83 1.9 5 4 H=.514

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

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? http://wks.uts.ohio-state.edu/sasdoc/

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

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