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›René Veenstra

›Department of Sociology

http://www.gmw.rug.nl/~veenstra

Dynamic Social Network Analysis

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The basics› What is a network?

• A graph in which…• we have a set of nodes (children, companies, web pages)…• connected by ties (friendship relations, product exchanges,

citations)

› Why do we look at networks?• to study relational data, considering simultaneously both

individuals connected by a tie • to see how ties combine: individuals are connected to others,

who themselves are also connected to others • to find and highlight statistical properties that characterize

structure and behavior of networked systems• to make predictions based on measured structural properties

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Network data› We commonly use

matrices containing the ties

› Example:

a1 has a tie to a2 and a5

a1

a2

a3

a4

a5

a6

a1

0 1 0 0 1 0

a2

1 0 0 0 0 0

a3

0 1 0 0 0 1

a4

1 1 0 0 0 0

a5

0 0 0 0 0 1

a6

1 1 1 1 1 0

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Non-directed and directed graphs

› Non-directed• e.g., romantic relationship, marriage ties

› Directed• e.g., friendship nominations, bullying

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Network parameters: Degree› In-degree:

• number of ties directed at the node• popularity of an actor• number of received nominations

› Out-degree: • number of ties going from the node• activity of an actor• number of given nominations

› Isolate:• Node without lines attached to it

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Network parameters

› Number of possible lines• non-directed: n (n-1)/2• directed: n (n-1)

› Density (ranges from 0 to 1)• the proportion of possible lines that are

actually present in the graph› Outdegree (density = 0.5 outdegree = 0)• models the density of the network

› Reciprocity (with friendship data usually positive)• a mutual tie: i chooses j and j chooses i.

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Network parameters: closure

› Transitivity (usually positive)• measure of triads• ‘a friend of a friend is a friend’

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Evolution of social networks

› Single observations are snapshots• Result of untraceable history• Explaining them has limited importance

› Longitudinal modeling offers promise for understanding network structure

› Structures of relations between actors that evolve

› Dynamics of social networks

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SIENA: Actor oriented approach› Analyzing longitudinal changes in networks

› At certain moments in time actors can make choices, based on the evaluation of their position in the network:• actors can change ties (selection processes)• actors can change their behavior (socialization or

influence processes)

› See also: • Steglich, C.E.G., Snijders, T.A.B., & West, P. (2006). Applying

SIENA. Methodology, 48-56.• Burk, W. J., Steglich, C. E. G., & Snijders, T. A. B. (2007).

Beyond dyadic interdependence. International Journal of Behavioral Development, 31, 397-404.

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Purpose of statistical modeling

› Investigate network evolution as function of:• Structural network effects (e.g., reciprocity,

transitivity)• Explanatory actor variables (e.g., gender,

aggression, victimization)• Explanatory dyadic variables (e.g., same-

gender, bullying relationship)› All effects control for each other› Without structural network effects, tests of

other effects would be unreliable

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Example data of Ernest Hodges

› 167 male actors (predominantly Hispanic and low SES background)

› Tie = friendship› Actor covariates: gender, aggression,

victimization, weapon carrying› 2 measurements: one year apart

Dijkstra, J.K., Lindenberg, S., Veenstra, R., & Hodges, E.V.E. Selection and influence processes in weapon carrying in early adolescence. The role of status, aggression, and vulnerability.

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Tie Changes Between Wave 1 and 2

Period 0=>0 0=>1 1=>0 1=>1 Missing1 ==> 2 22842 847 896 1610 1527 ( 6%)

Average degreeT1: 0.109T2: 0.095

Proportion of Reciprocated Ties: 2M/(2M+A) T1: 75% (2262 / 3020)T2: 70% (1718 / 2458)

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Prevalence of Weapon CarryingT1 T2(N=164) (N=138)

0 times 72.6% 69.6%1 time 4.9% 5.8%2-5 times 10.4% 8.7%6-10 times 2.4% 2.2%> 10 times 9.8% 13.8%

Period down up constant Missing

1 ==> 2 17 (29 steps) 24 (49 steps) 94 32

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SIENA Estimates and Standard Errors

› Network Effects: Est. SE1. Outdegree -1.411 (0.065) ***2. Reciprocity 1.434 (0.133) ***3. Transitivity 0.024 (0.001) ***

› Network Dynamics:4. Weapon carrying similarity (selection) 0.087 (0.117)Effect of weapon carrying on5. Friendship nominations received 0.117 (0.033) ***6. Friendship nominations given -0.065 (0.029) *

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SIENA Estimates and Standard Errors

› Behavioral tendencies: Est. SE7. Weapon Carrying Linear -1.100

(0.173) ***8. Weapon Carrying Quadratic 0.582

(0.090) ***

› Behavior Dynamics:9. Weapon carrying similarity (influence) 3.316 (1.864) ~10. Effect of Aggression T1 2.270 (1.370) ~11. Effect of Victimization T1 -0.246 (1.187)

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One-week Summer Course in Kansas› Kansas University Summer Institute in Statistics› one-week course (June 15-19, 2009) "Social Network

Dynamics“› taught by Tom Snijders› This will be the first workshop where the new version

of SIENA implemented as an R package will be taught

Topics: › statistical analysis of network dynamics for complete

networks› networks co-evolving with dependent actor variables

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SNA Community

Handbooks› Wasserman, S. & Faust, K. (1994). Social Network

Analysis: Methods and Applications. New York: Cambridge University Press.

› Carrington, P.J., Scott, J., & Wasserman, S. (2005) (eds.) Models and methods in Social Network Analysis. New York: Cambridge University Press.

Journal: Social NetworksConference: Sunbelt

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Thank you for your attention

Software and manual:http://stat.gamma.rug.nl/siena/