Social capital and Smallworlds

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Social capital and Small-worlds

• (ESRC funded project to begin in June 2008)

Principle Investigator Christina
Prell Collaborators Tom Snijders, Oxford
(Scientific Mentor) Alan Walker,
University of Sheffield (Institutional Mentor)
Mike Savage, University of Manchester
(social capital research group)
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Overarching themes/questions

• Previous research on social capital
• Linking this to small worlds literature
• Seem to be structural similarities between
  social capital networks and small-world
  networks
• Micro (or local) structures
• Similarity in appearance at the network (or
  global) level
• What other kinds of overlaps are there?
• Mechanisms leading to structures
• Outcome variables

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Earlier work on social capital

• Notions of closure and brokerage
• Closure or bonding (Putnam/Burt/Coleman)
• Brokerage or bridging (Putnam/Burt)
• Optimal version
• a mixture of cohesive subgroups with bridging
  ties.
• Putnam/Burt/Granovetter/Woolcook and Narayan

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• In short, brokerage and network closure can
  be brought together in a productive way...
  Closure describes how dense or hierarchical
  networks lower the risk associated with
  transaction and trust, which can be associated
  with performance.
• Brokerage describes how structural holes are
  opportunities to add value with bridges across
  the holes, which is associated with performance
  while brokerage across structural holes is the
  source of added value, closure can be critical to
  realizing the value buried in the structural
  holes. (Burt 2001, pg. 52)

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Granovetters forbidden triangle
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Triangles/triads and social capital
Brokerage Weak/bridging ties open triad or
2-star
Closure Strong ties, dense network closed triad
or triangle
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Small-worlds

• Milgram (67) you can reach anyone through just
  a few links
• Watts and Strogatz
• Large heterogeneous networks
• Small average path length (2-4 degrees)
• High Clustering coefficient(cohesive sub-groups)
• Low density (i.e. not many ties/edges in
  network)
• No dominate node
• Exists somewhere betweena connected caveman
  structure and a completely random one

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Small-Worlds

• Barabási and Albert Scale- free/small-world
  networks.
• Short paths
• Small number of nodes holding the majority of
  ties hubs
• Power law distributions
• History
• networks grow one node at a time
• The process of preferential attachment

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Scale-free hubs, no clusters
Modular cohesive sub-groups linked together with
a few ties (Similar to connected caveman and also
to Granovetters circles of friends and Burts
mixture of closure and brokerage)
Modular-scale-free
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Scale-free hubs, no clusters
Modular cohesive sub-groups linked together with
a few ties (Similar to Granovetters circles of
friends and Burts mixture of closure and
brokerage)
Modular-scale-free
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Scale-free hubs, no clusters
Modular cohesive sub-groups linked together with
a few ties (Similar to Granovetters circles of
friends and Burts mixture of closure and
brokerage)
Modular-scale-free small-worlds
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• Low density (-4.0)
• High presence of 2-stars (0.1)
• Very few 3-stars (-0.05)
• High presence of triangles (1.0)
• (more triangles than 2-stars)

Garry Robins, Philippa Pattison, and Jodie
Woolcock (2005) Global Network Structures from
Local Processes, AJS.
High clustering Short paths
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Structural similarities?

• Small Worlds Social Capital

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Similarities..????
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Similarities..????
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Similarities..????
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Similarities..????
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Similarities..????
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Other considerations.

• Not just about structure!
• Outcome variables
• Small worlds
• Resilience
• Robustness
• Social capital
• Well-being
• Performance
• Efficiency
• Getting by versus getting ahead
• Trust and reciprocity

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Other considerations

• Certain mechanisms leading to structures
• Preferential attachment
• Path dependence

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Small worlds asks Social capital

• We know that social capital is seen as emerging
  from networks that hold closure/brokerage
  structures (and that closure/brokerage can be
  seen as a structural attribute of small-worlds)
• Do these social capital networks hold other
  small world structural attributes?
• If so, do they have some of the same outcome
  variables we would expect for example, are these
  networks more resilient?

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Social capital asks small worlds

• We know that small-worlds tend to be more robust
  and resilient, but also
• In instances where small world networks are
  composed of human actors,
• are these networks also characterised by trust
  and reciprocity, etc. as social capital
  literature suggests?

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Questions are 2 parts

• Part 1 Structural question
• To what extent are social capital network
  structures similar to small-world network
  structures?
• Part 2 Outcomes and mechanisms
• Do small world networks have social capital
  outcomes?
• Do social capital networks have small world
  outcomes?
• What mechanisms (e.g. Preferential attachment)
  give rise to these structures and outcomes?

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Today an initial look at the structural question

• Through use of p
• Through use of a well-known data set found in
  UCINET data archives.
• Aim take an initial stab at structural
  considerations
• Use a familiar dataset

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Breiger Pattisons Florentine Families (subset
of John Padgetts data). Business Ties in
Florence circa 1430
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Marriage Ties in Florence circa 1430
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Average path length (for reachable pairs of
actors) 2.382 Average Clustering Coefficient
0.6 Density 0.13
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Other structural features p

• A model for social networks for testing the
  probability of certain structural tendencies in a
  given network.
• Are certain micro structures, such as 2-stars and
  triangles, more often observed in a real network
  than one might expect from chance?
• It also controls and conditions for how
  lower-level structures, such as reciprocity,
  might affect higher level ones, such as
  transitive triads/closed triads
• In doing so, p helps one uncover the relative
  contribution of each tendency to the overall
  network configuration.

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Same parameters tested in Robins, Pattison,
Kalish, and Lusher (2006), SN Robins, Pattison,
and Woolcock (2005) Global Network Structures
from Local Processes, AJS. Using SIENA.

• Density
• 2-stars
• 3-Stars
• Triangles (transitive triads)

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Results

• Estimates and SE
• Density -4.2416 (1.0974) -3.87
• 2-stars 1.0474
  (0.6386) 1.64
• 3-stars -0.6370
  (0.4026) -1.58
• transitive triads 1.3212
  (0.6403) 2.06
• Absolute value is greater than 2, so
  significant at 0 05 level.

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Breiger Pattisons Florentine Families (subset
of John Padgetts data). Business Ties in
Florence circa 1430
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In conclusion.

• Discussion of how social capital and small-worlds
  overlap and/or inform one another.
• Small example to illustrate some ways to begin
  exploring these overlaps.
• Next steps.
• More data!
• Gain more precision for some of the structural
  measures

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References

• Barabási, A.-L. 2002. Linked the new science of
  networks Perseus Pub., Cambridge, Mass.
• Barabási, L. 2000. The large-scale organization
  of metabolic networks. Nature 407651-654.
• Barabási, L., and R. Albert. 2001. Emergence of
  scaling and random networks. Science 286509-
  512.
• Breiger, R., and P. Pattison. 1986. Cumulated
  social roles The duality of persons and their
  algebras. Social Networks 8215-256.
• Burt, R. 2001. Structure Holes versus Network
  Closure as Social Capital, In K. C. N. Lin, and
  R. Burt (eds.) ed. Social Capital Theory and
  Research. New York Aldine de Gruyter.
• Burt, R. 2005. Brokerage and Closure An
  Introduction to Social Capital Oxford Oxford
  University Pres.
• Granovetter, M. 1973. The strength of weak ties.
  American journal of sociology 781360-1380.
• Narayan, D. 1999. Bonds and Bridges Social
  Capital and Poverty. Worldbank, Washington, D.C.
• Prell, C. 2003. Community networking and social
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  http//jcmc.indiana.edu/vol8/issue3/prell.html
• Prell, C. 2006. Social Capital as Network
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• Prell, C., Skvoretz, J. (forthcoming). Social
  capital on the triad level. Connections.
• Putnam, R.D. 1995. Bowling alone Americas
  declining social capital. Journal of democracy
  665-78.
• Putnam, R.D. 2001. Bowling Alone the collapse
  and revival of American community. London Simon
  Schuster.
• Robins, G., P. Pattison, and J. Woolcock. 2005.
  Small and other worlds Global network structures
  from local processes. American Journal of
  Sociology 110894-936.
• Robins, G., P. Pattison, Y. Kalish, and D.
  Lusher. An introduction to exponential random
  graph (p) models for social networks. Social
  Networks In Press, Corrected Proof.
• Watts, D.J. 1999. Networks, dynamics and the
  small world phenomenon. American Journal of
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• Watts, D.J. 2003. Six degrees the science of a
  connected age. 1st ed. Norton, New York.
• Watts, D.J., and S.H. Strogatz. 1998. Collective
  dynamics of small world networks. Nature
  393440-442.

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Small-Worlds result from the following
conditions

• Individuals seek more than one partner.
• At the same time, individuals do not have too
  many partners.
• This tension may describe how short paths emerge.
• A tendency toward clustering and structural
  balance.
• Neither too strong (or else too clique-like with
  too few short cuts)
• Nor too weak (or else not enough clustering in
  network)

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Egalitarian not dominated by a few hubs. Can
withstand targeted attacks better.
Aristocratic dominated by a few hubs. Can
withstand random attacks better.
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Granovetters circle of friends and forbidden
triangle
cellular networks started to also show high
clustering coefficients and short path lengths..
Granovetter lacked a complete map of the social
system?