Patterns & Paradox: Network Foundations of Social Capital James Moody Ohio State University...

Patterns & Paradox: Network Foundations of Social Capital

James MoodyOhio State University

Columbus, Ohio June 20th 2005

Network Foundations of Social CapitalIntroduction

“If we ever get to the point of charting a whole city or a whole nation, we would have … a picture of a vast solar system of intangible structures, powerfully influencing conduct, as gravitation does in space. Such an invisible structure underlies society and has its influence in determining the conduct of society as a whole.”

J.L. Moreno, New York Times, April 13, 1933

Source: Linton Freeman “See you in the funny pages” Connections, 23, 2000, 32-42.



Burt argues that social capital is a “useful metaphor,” explaining “how people do better because they are somehow better connected with other people,” and that we need to “cut beneath the metaphor to reason from concrete network mechanisms responsible for social capital” (Burt 2005, chap 1).

What are the “concrete network mechanisms” that create advantage for communities & organizations?

How do individual membership patterns shape community cohesion?

Can social capital increase as membership volume decreases?

1. Introduction2. Network Mechanisms & Social Capital3. Structural Cohesion 4. Networks Through Associations5. Effects of Pattern vs. Volume6. Simulating Association Networks7. Conclusions & Extensions

Network Foundations of Social CapitalOutline

Network Foundations of Social CapitalNetwork Mechanisms & Social Capital

Net

wor

k M

echa

nism

: Social Support

Social Influence

Diffusion

Direct Indirect

Companionship Community

Peer Pressure /Information

Cultural differentiation

Receiving / Transmitting

Spread through a population

Network Level:

Direct


Indirect


Net

wor

k C

hara

cter

istic

:

Direct IndirectNetwork Aspects of Social Capital:

“Position” “Connectivity”

Network Level:

Pattern

Volume

BrokerageCentrality

Group SegregationSocial ClosureStructural Cohesion

Network SizeNumber of Memberships

Network Density


Importance of Pattern:

These two networks are equivalent on any volume measure.



Net

wor

k M

echa

nism

:

Direct IndirectNetwork Aspects of Social Capital:

“Position” “Connectivity”

Network Level:

Pattern

Volume

BrokerageCentrality

Group SegregationSocial ClosureStructural Cohesion

Network SizeNumber of Memberships

Network Density

Network Foundations of Social CapitalStructural Cohesion

An intuitive definition of structural cohesion:

A collectivity is structurally cohesive to the extent that the social relations of its members hold it together.

The minimum requirement for structural cohesion is that the network be connected.

Add relational volume:




When focused on a single person, the network is fragile.




Spreading relations around the structure makes it robust to node removal.




Formal definition of Structural Cohesion:(a) A group’s structural cohesion is equal to the minimum number

of actors who, if removed from the group, would disconnect the group.

Equivalently (by Menger’s Theorem):

(b) A group’s structural cohesion is equal to the minimum number of independent paths linking each pair of actors in the group.


See Moody & White (2003) American Sociological Review 68:103-127

•Networks are structurally cohesive if they remain connected even when nodes are removed

Node Connectivity

0 1 2 3


As structural cohesion increases, fewer nodes are able to control resource flow within the network.

•Power is more evenly distributed because nobody controls access to network resources•Information flows more uniformly across the network

•Norms & Values should be proportionately more uniform

•Informal Social Control should be more uniform as there are fewer opportunities to free ride

The collectivity should take on a community character


See Moody & White (2003) American Sociological Review 68:103-127 for details & justifications

Structural cohesion gives rise automatically to a clear notion of embeddedness, since cohesive sets nest inside of each other.

17

1819

20

222

23

8

11

10

14

12

9

15

16

13

4

1

75

6

3

2


Connectivity

Connectivity Distribution


1

2

3

4

5

6

7

8

9

10

A

B

C

D

3 5

1

6 7

8

10

9

4

2

Person

A B

C D

Group

Network Foundations of Social CapitalNetworks Through Associations

People Groups

How do joint membership patterns shape networks of organizations?

If membership in one group strongly predicts membership in another group, then the resulting network will be constrained, leading to redundant ties within classes.

Network Foundations of Social CapitalEffects of Pattern vs. Volume

White

Rich Poor

Male

Female

Male

Female

Black

Rich Poor

Male

Female

Male

Female

Tight membership structures

How do joint membership patterns shape inter-organizational networks?

If membership in one group does not predict membership in another group, then the resulting network will be unconstrained, leading to multiple cross-class ties.

Network Foundations of Social CapitalEffects of Pattern vs. Volume

Male

White

Ric

h

Poo

r

Female

BlackLoose

membership structures

Goal: Explore the relative weight of pattern and volume effects in a stochastic individual-actor simulation.

Setup: The population is divided into a number of “classes,” and certain associations are typical to each class.

WhiteBlack

FemaleMale FemaleMale FemaleMale FemaleMale

PoorRich PoorRich

Total

Network Foundations of Social CapitalSimulating Association Networks: Setup

The pattern of group mixing is controlled by the probability of joining an association outside of one’s class, which is conditioned by the distance between each class. Here I contrast three distance models:

In-group-Out Group:Probability of joining any group from another class is 1-probability of joining a group typical for one’s own class.

Matching Attributes (Blau space model):Probability of joining any group from another class is proportional to the number of class attributes the two classes have in common (so a white male and a black male would be closer than a white male and a black female).

Nested Attributes (Master-status model):Probability of joining any group from another class is proportional to the distance in the class-branching tree. This implies a nested set of classes (gender within, class, within race, for example).



Simulation Process:1) Simulated actors join groups...

• Np = 4000

• Ng = 80• P(in-class) is distributed Poisson on class distance. Pattern effects

are controlled by the Poisson location parameter.• Number of groups each person joins is varied across simulations.

The distribution has a mode of 1 and is highly skewed. Volume effects are controlled by changing the mean & / or distribution of groups actors join.

2) …creating networks among organizations.• Membership creates a group-to-group networks of shared members.• Calculate the pair-wise connectivity distribution for all pairs in each

network

The simulation is repeated 500 times for each parameter setting.

Network Foundations of Social CapitalSimulating Association Networks: Results


In-Group / Out-Group model with moderate in-group bias

Inter-organizational ties

1

1.2

1.4

1.6

1.8

2

IG/OG Match Nested

(

Patt

ern)

/

(Vol

ume)

Relative effect of pattern & volume


Network Foundations of Social CapitalConclusions & Extensions

Can social capital increase if individual involvement decreases?

Yes

The carrying capacity of networks depends at least as much on the pattern of ties as on the volume of ties. If people are less involved but membership patterns are “loose” network connectivity can still be high.

Network Foundations of Social CapitalConclusions & Extensions: Direct Results

•Individual actions cannot be simply aggregated;•We must attend directly to how memberships construct organizational networks

•We cannot conclude from decreasing numbers of group memberships that the underlying network is less cohesive or that (this dimension) of social capital has decreased.

•If membership patterns have become looser at the same time, the two trends could balance out.

•The shape of the class-mixing model matters. Master-status gulfs are the hardest to bridge.

Network Foundations of Social CapitalConclusions & Extensions: Further Extensions

•Concatenation effects can be very rapid: the difference between a connected and disconnected system can rest on small individual changes

•Pay attention to higher-order moments: if we change the shape of the involvement distribution without changing volume, we get different networks (skew lowers cohesion).

•These effects are just as important for brokerage as it is for closure.

•The value of seeking structural holes depends entirely on the extent to which other people are acting similarly

Network Foundations of Social CapitalConclusions & Extensions

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