Social%20Cohesion%20and%20Connectivity:

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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
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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
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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

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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
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Why do Networks Matter?
Local vision
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Why do Networks Matter?
Global vision
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Why do Networks Matter?
Consider the following (much simplified) scenario

• Probability that actor i infects actor j (pij)is
  a constant over all relations 0.6
• S T are connected through the following
  structure

S
T

• The probability that S infects T through either
  path would be 0.09

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Probability of infection over independent paths

• The probability that an infectious agent travels
  from i to j is assumed constant at pij.
• The probability that infection passes through
  multiple links (i to j, and from j to k) is the
  joint probability of each (link1 and link2 and
  link k) pijd where d is the path distance.
• To calculate the probability of infection passing
  through multiple paths, use the compliment of it
  not passing through any paths. The probability
  of not passing through path l is 1-pijd, and thus
  the probability of not passing through any path
  is (1-pijd)k, where k is the number of paths
• Thus, the probability of i infecting j given k
  independent paths is

Why matter
Distance
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Probability of infection over non-independent
paths
- To get the probability that I infects j given
that paths intersect at 4, I calculate
Using the independent paths formula.
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Why do Networks Matter?
Now consider the following (similar?) scenario
S
T

• Every actor but one has the exact same number of
  partners
• The category-to-category (blue to orange) mixing
  is identical
• The distance from S to T is the same (7 steps)
• S and T have not changed their behavior
• Their partners partners have the same behavior
• But the probability of an infection moving from S
  to T is
• 0.148
• Different structures create different outcomes

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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.
• Ones risk for receiving/transmitting a good
  depends on ones position in the overall network
  (structural embeddedness)
• The strength and qualities of direct connections
  (direct embeddedness)

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Three Approaches to Network Structure
1. Small World Networks
Based on Milgrams (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.
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Three Approaches to Network Structure
1. Small World Networks
CLarge, L is Small SW Graphs

• High relative probability that a nodes contacts
  are connected to each other.
• Small relative average distance between nodes

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Three Approaches to Network Structure
1. Small World Networks
In a highly clustered, ordered network, a single
random connection will create a shortcut that
lowers L dramatically
Watts demonstrates that small world properties
can occur in graphs with a surprisingly small
number of shortcuts
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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.
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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)
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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)
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Three Approaches to Network Structure
2. Scale-Free Networks

• Scale-free networks can appear when new nodes
  enter the network by attaching to already popular
  nodes (called proportionate mixing in earlier
  epidemiology models).
• Scale-free networks are common (WWW, Sexual
  Networks, Email)

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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

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Three Approaches to Network Structure
2. Scale-Free Networks
Hubs make the network fragile to node disruption
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Three Approaches to Network Structure
2. Scale-Free Networks
Hubs make the network fragile to node disruption
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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 68103-127
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Three Approaches to Network Structure
3. 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.

• Five features
• A property describing how a collectivity is
  united
• It is a group level property
• The conception is continuous
• Rests on observed social relations
• Is applicable to groups of any size

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The minimum requirement for structural cohesion
is that the collection be connected.
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Add relational volume
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Add relational volume
When focused on one node, the system is still
fragile.
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Spreading relations around the structure makes it
robust to node removal.
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Three Approaches to Network Structure
3. Structural Cohesion

• Formal definition of Structural Cohesion
• A groups structural cohesion is equal to the
  minimum number of actors who, if removed from the
  group, would disconnect the group.
• Equivalently (by Mengers Theorem)
• A groups structural cohesion is equal to the
  minimum number of independent paths linking each
  pair of actors in the group.

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Three Approaches to Network Structure
3. Structural Cohesion

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

0
1
2
3
Node Connectivity
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Three Approaches to Network Structure
3. Structural Cohesion

• Identified in wide ranging contexts
• High School Friendship networks
• Biotechnology Inter-organizational networks
• Mexican political networks
• Kinship networks
• Structurally cohesive networks are conducive to
  equality and diffusion, since no node can control
  the flow of goods through the network.

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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
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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 78152-158
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Three Approaches to Network Structure
3. Structural Cohesion STD diffusion in Colorado
Springs
Epidemic Gonorrhea Structure
G410
Source Potterat, Muth, Rothenberg, et. al.
2002. Sex. Trans. Infect 78152-158
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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 78152-158
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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
7
5
12
13
6
14
15
17
16
18
19
20
2
22
23
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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).
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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
• Briegers (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.

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Getting Data Duality of Persons and Groups
Person
Group
A
B
D
C
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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 theyve 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.

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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.

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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
SES
GPA
Fight
College
Drinking
Same Sex
Transitivity
Same Race
Both Smoke
Same Clubs
Intransitivity
Same Grade
Reciprocity
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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
edge connectivity (valued) of the group to group
network. The relative edge connectivity is
robust to sampling
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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.
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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.
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Groups differ in the extent to which members are
jointly involved in other groups. We dont
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)
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Structural Implications of group membership
Two hypothetical examples.
A sample of 4000 people, who each visit an
average of 1.4 bars.
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Structural Implications of group membership
Two hypothetical examples.
Tight membership mixing
Loose membership mixing
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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.
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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.

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