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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.
Network Foundations of Social CapitalIntroduction
Network Foundations of Social CapitalIntroduction
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
Network Foundations of Social CapitalNetwork Mechanisms & Social Capital
Indirect
Network Foundations of Social CapitalNetwork Mechanisms & Social Capital
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
Network Foundations of Social CapitalNetwork Mechanisms & Social Capital
Importance of Pattern:
These two networks are equivalent on any volume measure.
Network Foundations of Social CapitalNetwork Mechanisms & Social Capital
Network Foundations of Social CapitalNetwork Mechanisms & Social Capital
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:
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.
When focused on a single person, the network is fragile.
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.
When focused on a single person, the network is fragile.
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.
Spreading relations around the structure makes it robust to node removal.
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.
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.
Network Foundations of Social CapitalStructural Cohesion
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
Network Foundations of Social CapitalStructural Cohesion
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
Network Foundations of Social CapitalStructural Cohesion
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.
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75
6
3
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Network Foundations of Social CapitalStructural Cohesion
Connectivity
Connectivity Distribution
Network Foundations of Social CapitalStructural Cohesion
1
2
3
4
5
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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).
Network Foundations of Social CapitalSimulating Association Networks: Setup
Network Foundations of Social CapitalSimulating Association Networks: Setup
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
Network Foundations of Social CapitalSimulating Association Networks: Results
In-Group / Out-Group model with moderate in-group bias
Inter-organizational ties
Network Foundations of Social CapitalSimulating Association Networks: Results
Network Foundations of Social CapitalSimulating Association Networks: Results
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 CapitalSimulating Association Networks: Results
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
Form or Content?