Social Cohesion and Connectivity: Diffusion Implications of Relational Structure

1. Social Cohesion and Connectivity: Diffusion Implications of Relational Structure James Moody The Ohio State University Population Association of America Meetings Minneapolis Minnesota, May 1 – 3, 2003

2. Why do Networks Matter? “To speak of social life is to speak of the association between people – their associating in work and in play, in love and in war, to trade or to worship, to help or to hinder. It is in the social relations men establish that their interests find expression and their desires become realized.” Peter M. Blau, Exchange and Power in Social Life, 1964 "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

3. Why do Networks Matter? The importance of networks is well recognized in demographic work: • Behrman, Kohler, and Watkins (2003) Demography 713 – 738 • Lusyne, Page and Lievens (2001). Population Studies 281-289 • Astone, NM, CA Nathanson, R Schoen, and YJ Kim. (1999) Population and Development Review 1-31 • Goldstein (1999) Demography 399-407 • Entwisle, Rindfuss. Guilkey,Chamratrithirong; Curran and Sawangdee (1996) Demography 1-11

4. Why do Networks Matter? Direct Indirect Mechanism: Social Support Companionship Community Cultural differentiation Social Influence Peer Pressure / Information Receiving / Transmitting Population distribution Diffusion Local “Ego-network” Global or partial network Data

5. Why do Networks Matter? Local vision

6. Why do Networks Matter? Global vision

7. Why do Networks Matter? • Combining alternative mechanisms with levels of observation, “Why networks matter?” reduces to two classes of related questions: • Those dealing with global network structure. • The global structure of the network affects how goods can travel throughout the population. The key elements for diffusion are average path distance and connectivity. • Those dealing with individual or group position. • One’s “risk” for receiving/transmitting a good depends on one’s position in the overall network (“structural embeddedness”) • The strength and qualities of direct connections (“direct embeddedness”)

8. Three Approaches to Network Structure 1. Small World Networks Based on Milgram’s (1967) famous work, the substantive point is that networks are structured such that even when most of our connections are local, any pair of people can be connected by a fairly small number of relational steps.

9. Three Approaches to Network Structure 1. Small World Networks C=Large, L is Small = SW Graphs • High relative probability that a node’s contacts are connected to each other. • Small relative average distance between nodes

10. Three Approaches to Network Structure 2. Scale-Free Networks Across a large number of substantive settings, Barabási points out that the distribution of network involvement (degree) is highly and characteristically skewed.

11. Three Approaches to Network Structure 2. Scale-Free Networks Many large networks are characterized by a highly skewed distribution of the number of partners (degree)

12. Three Approaches to Network Structure 2. Scale-Free Networks Many large networks are characterized by a highly skewed distribution of the number of partners (degree)

13. Three Approaches to Network Structure 2. Scale-Free Networks Colorado Springs High-Risk (Sexual contact only) • Network is power-law distributed, with l = -1.3

14. Three Approaches to Network Structure 2. Scale-Free Networks Hubs make the network fragile to node disruption

15. Three Approaches to Network Structure 2. Scale-Free Networks Hubs make the network fragile to node disruption

16. Three Approaches to Network Structure 3. Structural Cohesion James Moody and Douglas R. White. “Structural Cohesion and Embeddedness: A hierarchical Conception of Social Groups” American Sociological Review 68:103-127

17. Three Approaches to Network Structure 3. Structural Cohesion The minimum requirement for structural cohesion is that the collection be connected.

18. Three Approaches to Network Structure 3. Structural Cohesion Add relational volume:

19. Three Approaches to Network Structure 3. Structural Cohesion Add relational volume: When focused on one node, the system is still fragile.

20. Three Approaches to Network Structure 3. Structural Cohesion Spreading relations around the structure makes it robust to node removal.

21. Three Approaches to Network Structure 3. 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.

22. Three Approaches to Network Structure 3. Structural Cohesion • Networks are structurally cohesive if they remain connected even when nodes are removed 2 3 0 1 Node Connectivity

23. Three Approaches to Network Structure 3. Structural Cohesion Probability of infection by distance and number of paths, assume a constant pij of 0.6 1.2 1 10 paths 0.8 5 paths probability 0.6 2 paths 0.4 1 path 0.2 0 2 3 4 5 6 Path distance

24. Three Approaches to Network Structure 3. Structural Cohesion STD diffusion in Colorado Springs Endemic Chlamydia Structure Source: Potterat, Muth, Rothenberg, et. al. 2002. Sex. Trans. Infect 78:152-158

25. Three Approaches to Network Structure 3. Structural Cohesion STD diffusion in Colorado Springs Epidemic Gonorrhea Structure G=410 Source: Potterat, Muth, Rothenberg, et. al. 2002. Sex. Trans. Infect 78:152-158

26. Three Approaches to Network Structure 3. Structural Cohesion STD diffusion in Colorado Springs Epidemic Gonorrhea Structure Source: Potterat, Muth, Rothenberg, et. al. 2002. Sex. Trans. Infect 78:152-158

27. Three Approaches to Network Structure 3. 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

28. Three Approaches to Network Structure 3. Structural Cohesion • Structural Embeddedness has proved important for: • Adolescent Suicide • Adolescent females who are not members of the largest bicomponent are 2 times as likely to contemplate suicide (Bearman and Moody, 2003) • Weapon Carrying • Adolescents who are not members of the largest bicomponent are 1.37 times more likely to carry weapons to school (Moody, 2003) • Adolescent attachment to school • Embeddedness is the strongest predictor of attachment to school (Moody & White, 2003), which is a strong predictor of other health outcomes (Resnick, et. al, 1997).

29. Getting Data: Duality of Persons and Groups • While global network position matters fundamentally, collecting global network data on (most) social relations is very expensive and time consuming. • First priority: develop network sampling and modeling schemes. This work is underway. • Identify alternative relations with long-lasting traces • Kinship records • Public interaction (Frank & Yasumoto, 1998) • Identify cohesion through co-membership • Brieger’s (1974) work on the duality of persons and groups demonstrated how we can link people (groups) to each other through membership. • Data are surprisingly abundant – almost any list can form a basis for co-membership. • The resulting group-level network is robust to standard sampling methods.

30. 1 4 5 3 2 A 3 2 1 4 9 B 6 7 5 10 6 8 C 7 8 9 D 10 Getting Data: Duality of Persons and Groups Person Group A B D C

31. Getting Data: Duality of Persons and Groups • Advantages of affiliation networks: • Ease of data collection. • Data on activities / presence / membership is easy to collect. A simple list of what people do / where they go is all that is needed. Examples include: • Formal organizations (clubs, churches, workplaces, etc.) • Event attendance (Parties they’ve been at recently, funerals, etc.) • Common meeting places (bars they frequent, where they met most recent partner, etc.) • Can be time-stamped for greater mixing accuracy • Sampling. • The resulting data are simply a n-way involvement cross-tabulation. This is a frequency table, which at the group-to-group level, is often quite robust to individual-level sampling, even in the face of heavily skewed involvement levels.

32. Getting Data: Duality of Persons and Groups • Disadvantage of affiliation networks: • Co-presence does not necessarily imply interaction • The resulting network can be thought of as a likely field of potential interaction, but does not record interaction itself. • This level of potential can be modeled, however, by including a basic ego-network module to then model the association between interaction and co-membership. • In general, we can also make some reasonable assumptions about the relation between interaction and membership based on (a) group size and (b) amount of time spent in the organization.

33. Getting Data: Duality of Persons and Groups Network Model Coefficients, In school Networks 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 GPA SES Fight College Drinking Same Sex Transitivity Same Race Both Smoke Same Clubs Intransitivity Same Grade Reciprocity

34. 4 5 3 A B 2 1 9 6 7 10 8 D C Getting Data: Duality of Persons and Groups The resulting “networks” are cross-tabulations of the number of people that belong to each group: In general, the minimum node connectivity of the person to person network is going to equal the edgeconnectivity (valued) of the group to group network. The relative edge connectivity is robust to sampling

35. Structural Implications of group membership There is a strong connection between the literature on “Social Capital” and group membership, which provides a theoretical link between notions of structural cohesion, ideational diffusion, and the duality of groups. Most research on the community building effects of group membership focus on relational volume (c.f. Putnam, 2000). However, to the extent that our interest is in how group membership creates structurally cohesive settings, interaction pattern is more important than volume. Suggestions about the structure of modern life (Pescosolido & Rubin, 2000), suggest that membership patterns should generate loosely coupled group structures.

36. Structural Implications of group membership • Structural cohesion increases when membership in various groups are uncorrelated. • If membership in group i predicts membership in group j (membership structure is tight), then the resulting groups will be nested. • For example, if all Kiwanis members are also Methodists while all Shriners are Catholic • If membership in group i is unrelated to membership in group j, then the resulting network will be structurally cohesive, as unconstrained membership links groups across many domains.

37. Groups differ in the extent to which members are jointly involved in other groups. We don’t currently have good empirical data on membership tightness, though it should be easy to calculate if collected properly. An untested empirical claim: Membership tightness has declined in the last 100 years. Paxton (2002)

38. Getting Data: Duality of Persons and Groups What types of “groups” might be of interest to population researchers? • Village – to – village networks (Entwisle et al, Demography 1997) If people marry, work, or attend services/festivals across villages, then the village-village links can form a probable contact network.

39. Getting Data: Duality of Persons and Groups What types of “groups” might be of interest to population researchers? • Mixing location. If we know where people ‘hook up’ to find partners, we can identify potential STD cores.