Social Network Analysis

Social Network Analysis

Fred Stutzman

Overview General Introduction

Disciplinary perspectives Terms and Definitions

Elements of a social network

Analytic Techniques Data collection, software

Basic Analysis Descriptive measures

Advanced Analysis Block Models, ERGM’s

The Social Network Perspective What is a social network?

Wasserman and Faust: “The social network perspective encompasses theories, models and applications that are expressed in terms of relational concepts and processes. That is, relations defined by linkages among units are a fundamental component…”

Wellman and Giulia: “Social network analysis treats personal communities as networks whose composition, structure, and contents are defined from the standpoint of (a usually large sample of) focal individuals at their centers.”

Burt: “Network models describe the structure of one or more networks of relations within a system of actors.”

The Social Network Perspective Personal Networks

Ego-centric networks defined at the individual level

Behavioral Networks Networks as represented in

activity, socio-technical systems

Organizational Networks Networked relations between

macro-level structures Online Social Networks

Publicly articulated networks as represented in systems

Fundamental Concepts Elements of a Social Network

Actor: Actors are discrete individual, corporate, or collective social units (among others; also: node, vertex) Individual: A Facebook friend, a romantic partner Corporate: Companies, government agencies,

universities Collective social units: Groups that can be

represented as a node on a graph

The actor represents the tie-generating unitand is therefore flexibly interpretable

Quoting (Wasserman & Faust, 1994)

Fundamental Concepts Elements of a Social Network

Relational Tie – Can be directional, weighted (also: line, arc, edge) Liking or friendships Transfer of resources Association or affiliation Behavioral interaction Movement between places Physical connection Formal relations Biological relationship

Quoting (Wasserman & Faust, 1994)

Fundamental Concepts Complex ties

Edge: Undirected line Arc: Directed line Loop: Line that ties vertex to

self Multiple: Directed arc occurring

multiple times Graph types

Simple undirected graph: No directional ties, loops, multiple lines

Simple graph: No multiple lines Network: Complex graph

Fundamental Concepts Elements of a Social Network

Groupings – The power of network analysis lies in the ability of model relationships among systems of actors Dyad: Relationship btw/ 2 actors Triad: Three actors and

potential ties within Subgroups: Larger groupings

of actors within the network Groups: Finite collections of

actors Partitions: Collections assigned

categorical value

Quoting (Wasserman & Faust, 1994)

Elements of a Social Network The social network represents the finite sets

of actors and the relations defined between them Actors Ties Groupings

What kind of questions can we ask of social network data?

Quoting (Wasserman & Faust, 1994)

Types of Social Networks One-mode network: Relations between a

single set of actors Marriage networks between people Transactions between companies Movement between places

Two-mode network: Relations between two sets of actors Donor relationships between corporations and

organizations Two-mode network: Affiliation network (one

actor/one event) Memberships in clubs Participation on a board of directorsQuoting (Wasserman & Faust, 1994)

Types of Social Networks Ego-centric or “personal” networks

A network with a focal actor (the “ego”) and “alters” who have connections to the ego Bearman/Moody study: Sexual relations w/alters General Social Survey: “From time to time, most people

discuss important matters with other people.  Looking back over the last six months who are the people with whom you discussed matters that are important to you?

Fischer: Relationship between geographical setting and support provided by the network

Gulia and Wellman: Supportive nature of ‘net contacts Ellison, Steinfeld and Lampe: Socially supportive

outcomes of Facebook use

Quoting (Wasserman & Faust, 1994)

Analytic Techniques How to collect social network data?

Personal network questionnaires Position generators Administrative records Organizational charts Secondary analysis Socio-technical systems

Analytic Techniques What does SNA data look like?

Edge lists[1,2 1,3 3,2]

Adjacency matrix (symmetric)

1 2 3

1 - 1 1

2 1 - 1

3 1 - -

Analytic Techniques Software for Analysis

Large number of software packages available for SNA Popular packages

Pajek: http://vlado.fmf.uni-lj.si/pub/networks/pajek/ UCINet: http://www.analytictech.com/ucinet/ Gephi: http://gephi.org/ Also: ORA, NodeXL, Network Workbench

Advanced packages Statnet and iGraph packages in R (highly recommended):

http://csde.washington.edu/statnet/ JUNG, NetworkX (Libraries for Java and Ruby, C++ Lib?)

Web tools Many Eyes

http://manyeyes.alphaworks.ibm.com/manyeyes/

Analyzing a Social Network Basic properties of social networks

Descriptive statistics: How many actors, how many ties?

Degree centrality: How many ties does each actor have; what kinds of actors have lots of ties, few ties. Are more ties always better?

Betweenness centrality: The connective properties of actors, hubs and authorities Better to connect two disparate groups?

Closeness centrality: Path length between actors Better to be closer to some people?

Network centrality: Average path length to traverse a network Shorter paths better?

Quoting (Wasserman & Faust, 1994)

Network properties

Descriptive: How many actors, ties; Degree centrality: How many ties on average;Betweenness: How connective; Closeness centrality: Path length between; NetworkCentrality: Avg path length of the network

Quoting (Wasserman & Faust, 1994)

Advanced Analysis Block Modeling

Examines the relations between classes of vertices (nodes)

Explores and compares the connective properties of classes, exploring density patterns

Two approaches: Random start and Optimized

Amenable to hypothesis testing with the bootstrap

Advanced Techniques Random Graph Comparison

Allows for tests of the associational aspects of categories (partitions), compared to exponential random graph

CDF of tie 0->1, Binomial dist Amenable to MLE, though

computationally intensive MCMC Simulation Modeled as log-odds Statnet in R

The Personal Network Summarizing the social network

Components: Actors, Ties, Relationships and Groups

Modes: One-Mode, Two-Mode Measures: How many connections, who has the

important connections, how dense is the network? Instruments: Name generators, position

generators, scales Outcomes: Social support, social capital, and a

host of others.

Why is the personal network important?

“Classic” SNA Studies Bearman, P. S., Moody, J., and Stovel, K. (2004). Chains

of Affection: The Structure of Adolescent Romantic and Sexual Networks. American Journal of Sociology, 110(1), 44--91.

Padgett, J. and Ansell, C. K. (1993). Robust Action and the Rise of the Medici. American Journal of Sociology, 98(6), 1259--1319.

Framingham Heart Study in Christakis, N. and Fowler, J. (2009). Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. New York, NY: Little Brown and Co.

Wellman’s East York Studies, Fischer’s Personal Networks in Cities and Towns

Adamic, L., Buyukkokten, O., and Adar, E. (2003). A Social Network Caught in the Web. First Monday, 8(6).

Resources Useful Mailing Lists

SOCNET CITASA (ASA)

Websites INSNA: http://www.insna.org/ SUNBELT Conference: http://www.insna.org/sunbelt

/ Recommended Texts

De Nooy’s et al.’s Pajek text Wasserman and Faust’s Social Network Analysis Easley and Kleinberg’s Networks, Crowds and

Markets