Patterns & Paradox: Network Foundations of Social Capital James Moody Ohio State University Columbus, Ohio June 20

Patterns & Paradox: Network Foundations of Social Capital James Moody Ohio State University Columbus, Ohio June 20th 2005

Network Foundations of Social Capital Introduction “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

Network Foundations of Social Capital Introduction Source: Linton Freeman “See you in the funny pages” Connections, 23, 2000, 32-42.

Network Foundations of Social Capital Introduction • 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?

Network Foundations of Social Capital Outline • Introduction • Network Mechanisms & Social Capital • Structural Cohesion • Networks Through Associations • Effects of Pattern vs. Volume • Simulating Association Networks • Conclusions & Extensions

Network Level: Direct Indirect Social Support Companionship Community Peer Pressure / Information Cultural differentiation Network Mechanism: Social Influence Receiving / Transmitting Spread through a population Diffusion Network Foundations of Social Capital Network Mechanisms & Social Capital

Network Foundations of Social Capital Network Mechanisms & Social Capital Direct

Network Foundations of Social Capital Network Mechanisms & Social Capital Indirect

Network Foundations of Social Capital Network Mechanisms & Social Capital Network Level: Network Aspects of Social Capital: Direct Indirect Network Size Number of Memberships Network Density Volume Network Characteristic: “Position” “Connectivity” Group Segregation Social Closure Structural Cohesion Pattern Brokerage Centrality

Network Foundations of Social Capital Network Mechanisms & Social Capital Importance of Pattern: These two networks are equivalent on any volume measure.

Network Foundations of Social Capital Network Mechanisms & Social Capital Network Level: Network Aspects of Social Capital: Direct Indirect Network Size Number of Memberships Network Density Volume Network Mechanism: “Position” “Connectivity” Group Segregation Social Closure Structural Cohesion Pattern Brokerage Centrality

Network Foundations of Social Capital Structural 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.

Network Foundations of Social Capital Structural 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. Add relational volume:

Network Foundations of Social Capital Structural 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 Capital Structural 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 Capital Structural Cohesion • Formal definition of Structural Cohesion: • 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): • 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

Network Foundations of Social Capital Structural Cohesion • Networks are structurally cohesive if they remain connected even when nodes are removed 2 3 0 1 Node Connectivity

Network Foundations of Social Capital Structural 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 See Moody & White (2003) American Sociological Review 68:103-127 for details & justifications

Network Foundations of Social Capital Structural Cohesion Structural cohesion gives rise automatically to a clear notion of embeddedness, since cohesive sets nest inside of each other. 2 3 1 9 10 8 4 11 5 7 12 13 6 14 15 17 16 18 19 20 2 22 23

Network Foundations of Social Capital Structural Cohesion Connectivity Distribution Connectivity

1 4 5 3 2 A 3 2 1 4 9 B 6 7 Person 5 10 6 8 C 7 Group 8 A B 9 D 10 D C Network Foundations of Social Capital Networks Through Associations People Groups

Network Foundations of Social Capital Effects of Pattern vs. Volume 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. Tight membership structures White Black Rich Poor Rich Poor Male Male Male Male Female Female Female Female

Black White Loose membership structures Poor Rich Male Female Network Foundations of Social Capital Effects of Pattern vs. Volume 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.

Total White Black Female Female Female Female Poor Poor Male Male Male Rich Rich Male Network Foundations of Social Capital Simulating Association Networks: Setup 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.

Network Foundations of Social Capital Simulating 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 Capital Simulating Association Networks: Setup • Simulation Process: • 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. • …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 Capital Simulating Association Networks: Results

Network Foundations of Social Capital Simulating Association Networks: Results In-Group / Out-Group model with moderate in-group bias Inter-organizational ties

Network Foundations of Social Capital Simulating Association Networks: Results

2 1.8 1.6 1.4 1.2 1 IG/OG Match Nested Network Foundations of Social Capital Simulating Association Networks: Results Relative effect of pattern & volume b (Pattern) / b (Volume)

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 Capital Conclusions & Extensions Can social capital increase if individual involvement decreases?

Network Foundations of Social Capital Conclusions & 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 Capital Conclusions & 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 Capital Conclusions & Extensions Form or Content?

Patterns & Paradox: Network Foundations of Social Capital James Moody Ohio State University Columbus, Ohio June 20