Introduction to social network analysis - · PDF fileIntroductiontosocialnetworkanalysis Introduction Motivation Networksforbehaviourchange: smokingprevention...

Introduction to social network analysis

Paola Tubaro

University of Greenwich, London

26 March 2012

Introduction to social network analysisIntroduction

Introducing SNA

Rise of online social networkingservices:⇒ social networks to the fore.New interest for social networkanalysis (SNA).Yet networks have always existed!Likewise, SNA now has a longhistory.

Understand what SNA is.Understand how you could useit.Learn basic principles andmeasures.

Outline

1 Introduction

2 What is SNA

3 Data

4 Network metrics

5 Further readings

Motivation

What can SNA be used for?

Improvements in organisational performance.

Policy interventions for behaviour change;

Motivation

The organisational chain of a company

Motivation

Formal chart vs. network

With whom do you discuss issues important to your work?

Motivation

Senior people relatively peripheral (Barry): removed from day-to-day activities of the group.

Motivation

The very central role of Nick (what if he moves to another job?)

Motivation

Product 1 division relatively separate from overall network.

Motivation

Interventions

Using network data to improve flows of communication and coordination in the organisation.

Motivation

Networks for behaviour change: smoking prevention

Network of friendships among sixth grade pupils.

Squares = girls, circles = boys; blue = smokers, red = non-smokers. Valente et al. 2003.

Motivation

Use popular pupils (“opinion leaders”) to reduce smokingin adolescents

Identify most popular pupils in class;

Recruit and train them;

Use them to spread the message.

Valente et al. 2003: network method effective in reducing adolescents’smoking.

Introduction to social network analysisWhat is SNA

Defining SNA

An approach to human behaviours and social interactions.

A set of specific analytical and statistical methods.

A special type of data (and techniques of data collection).

A set of visualisation tools.

What is a network

What is a network —a formal definition

= A set of units (nodes) connectedby one or more relations (ties)

What is a node?⇒ Depends on setting: person,group/organisation, object.

What is a tie?⇒ A relation or a shared trait:friendship, advice, exchange,co-work.

What is a network

Graphs and networks

Circles (A, B) represent nodes.

Lines (e.g. between A and B) representties/edges.

Graph visualizes the whole structure ofties of a defined group.

Graphical conventions (colours, size ofnodes and/or ties) can be added to showattributes.

For example: if this is a network offriendship, blue = boys, red = girls.

What is a network

Graphs and networks

Circles (A, B) represent nodes.

Lines (e.g. between A and B) representties/edges.

Graph visualizes the whole structure ofties of a defined group.

Graphical conventions (colours, size ofnodes and/or ties) can be added to showattributes.

For example: if this is a network offriendship, blue = boys, red = girls.

What is a network

Isolates, dyads and triads

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Isolate Dyad Triad

The network perspective

A new perspective

SNA requires a change of mindset withrespect to other social science approaches.

Emphasis is on relationships, notattributes.

Not just dyadic relationships (just A andB), but dyadic relationships as embeddedin a whole set of relationships.

A new perspective

Embedded relationships

Figure: Suppose the relationship represented here is friendship. How may friendship between A and B vary in thesethree different contexts?

Triads

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Intransitive Transitive 3-cycles

Intransitive: Only bilateral ties.

Transitive: A friend of my friend is my friend.

Three-cycles: a form of generalized exchange.

Triads

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Intransitive Transitive 3-cycles

Intransitive: Only bilateral ties.

Transitive: A friend of my friend is my friend.

Three-cycles: a form of generalized exchange.

Network effects, more globally

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For example, those who attract many choices will attract even more infuture (reputation effect, “Matthew” effect).

Does a high (and growing) number of friends have advantages /disadvantages?

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Summary

Now you know:

What a network is;

Correspondence between a network and a graph;

Difference between triadic and dyadic structures;

Global effects of network structure.

Introduction to social network analysisData

Network data

Data format:How network data look likeHow they differ from other social science dataFrom data to graph

Data collection:Name generators/interpretersArchivesWeb crawlers

Data format

Data type 1: Ego networks

The whole set of contacts (alters) ofone person or entity (ego).

Usually includes attributes of altersand ties between them.

Usually collected for a sample of egos(e.g. in a survey).

Typically, graphically represented withego at its centre (star-shaped).

Data format

Example: Ego networks to discover “hidden” populations

Enrolling HIV+ persons to participate in vaccine preparedness study through their networks. Valente, 2010.

Data format

Data type II: Whole networks

Mapping the whole set of ties of aparticular group, setting or population.

Not focused on one particular personor entity.

Network boundaries must bewell-defined.

Examples: network of friends in aclassroom; network ofknowledge-sharing between employeesof an organisation.

Data format

Data storage: traditional social science

Social science data are usually represented in the form of a rectangulartable, where each row is an observation, each column is a variable: For

example:

name age gender marriedJane 25 0 0Mary 31 0 0Bob 29 1 1Sue 28 0 1Alan 32 1 0Tom 29 1 1

Data format

Network data storage I: matrix

Network data can be stored as a n-by-n square matrix with all nodeslisted in both columns and rows.The value of cell (i, j) in the matrix indicates whether the node i and thenode j are connected (1) or not (0).The diagonal is meaningless.

For example, for a friendship network:

Jane Mary Bob Sue Alan TomJane 1 1 0 0 0Mary 1 0 1 0 0Bob 1 0 0 1 0Sue 0 1 0 1 0Alan 0 0 0 1 1Tom 0 0 0 0 1

Data format

Data storage II: Edge list

The edge list stores each pair of connected nodes in a single row of atable.

For example, for the same friendship network:

ego alterJane MaryJane BobMary SueBob AlanAlan TomAlan Susan

Data format

Which format to choose

Most network analysis packages support both formats.

Some provide conversion facilities (e.g. UCINET: edge list tomatrix).

It is usually possible to combine network data (in matrix or edge listformat) and attributes.

A rectangular table is usually needed for attribute data —as intraditional social science.

Data format

Some general rules

Matrix visually appealing when nodeset is small, but difficult tohandle when it is large (because all possible pairs must be explicitlyincluded).

With large node sets, edge list is more convenient (because onlyexisting ties need to be listed).

Data format

Tie data I

Directed ties:

Tie goes from one node to another, butnot necessarily back.

E.g. Advice-giving, money-lending.

Usual graphical representation: arrow.

When directed ties do go in bothdirections, they are reciprocal ties.

Usual graphical representation: doublearrow.

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Data format

Tie data I

Directed ties:

Tie goes from one node to another, butnot necessarily back.

E.g. Advice-giving, money-lending.

Usual graphical representation: arrow.

When directed ties do go in bothdirections, they are reciprocal ties.

Usual graphical representation: doublearrow.

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Data format

Tie data II

Undirected ties:

Ties are mutual by definition.

E.g. Siblings, co-workers.

Usual graphical representation: line.

Data format

Undirected ties: matrix is symmetric

Data format

Directed ties: matrix is NOT symmetric

Data format

Binary and valued ties

Binary ties indicate presence or absence of tie

Valued ties can be stronger or weaker, undersome definition of strength:

Emotional closeness;Frequency of contact;Duration of Relationships.

Graphically: line (arrow) thickness oftenrepresents strength of tie.

Data format

Storing valued ties in a edge list

The edge list can include a third column with attributes of each tie.

In our friendship example, we can include duration of friendship:

ego alter duration(years)

Jane Mary 5Jane Bob 2Mary Susan 3Bob Alan 1Alan Tom 2Alan Susan 2

Data format

Storing valued ties in a matrix

Instead of 0-1 values, the matrix has different values depending onduration of the relationship:

Data format

Graphs

Basic principles of graph representationare simple (nodes and edges).

But graph visualisation is a complexproblem in computer science.

Which representation is most suitable fordetecting network structure andproperties?

Circle

Data format

Graphs

Fruchtermann-Rheinhold

Data format

Graphs

Kamada-Kawai

Data format

Graphs

Spring

Data format

Graphs

Data format

Now you know:

Format for network data: square matrix, rectangular matrix, edgelist.

Difference between Ego and whole networks.

Directed and undirected ties.

Binary and valued ties.

Graphical conventions to represent these different data.

Data collection

Collecting network data

Networks are built from nodes and the ties between them.

Who are the nodes?

What are the ties?

How to elicit information?

Data collection

How to identify nodes

Ego-network data collections often included in larger surveys.

Whole network data collection requires defining network boundaries,for example:

Members of an organisation;Students of one school;Attendees of one particular event.

N.B. collection of whole network data needs to be exhaustive–sensitive to response rate.

Data collection

Collecting network data through surveys: name generatorsand interpreters

Name generators are questions to elicit respondents’ alters, for example:

From time to time, most people discuss important matterswith other people. Looking back of the last six months, whoare the people with whom you discussed matters important toyou. Just tell me their names or initials.(General Social Survey, 1985)

Can be accompanied by name interpreters to report alter characteristicsand identify ties between alters.

Figure: A name generator with a graphical interface in a web-based survey; research project ANAMIA.

Data collection

Collecting network data through surveys: rosters

Provide respondents with a list of potential network members and askthem to choose from the list those to whom they are tied, for example:

Here is the list of all the members of your Firm.Would you go through this list, and check the names of thoseyou socialize with outside work. You know their family, theyknow yours, for instance. I do not mean all the people you aresimply on a friendly level with, or people you happen to meetat Firm functions.(Lazega, 2001)

Data collection

Collecting network data through surveys: rosters (cont.)

Used for whole network studies.

Also useful as a memory-aid.

Requires the researcher to have a complete list of nodes from start.

Only feasible for relatively small networks (e.g. schools, companies).

Data collection

Collecting network data from archives

For example: contract data from companies’ financial statements;citations data, from publishers’ portals.

Depends on the quality of the archive and the actual availability ofnetwork information.

Need to ensure definition of ties is consistent and data are reporteduniformly across all nodes.

Need to ensure completeness (for whole networks).

Figure: A citations network. From a study of the literature on pro-anorexic websites over ten years, with a corpusof 60 scientific articles. Casilli, Tubaro and Araya (2012), ANAMIA.

Data collection

Webcrawling

Using dedicated software to retrieve websites and the links betweenthem.

Increasingly popular with the rise of web-based networks, onlinesocial networking services, the study of the Internet as a network.

Defining network boundaries may be difficult.

Frequent need for manual verification of data quality.

Privacy protection issues.

Figure: A map of the pro-anorexic web sphere in France. F. Pailler, D. Pereira, ANAMIA.

Data collection

Now you know:

Different ways of collecting network data: surveys, archives,webcrawling.

All have advantages and disadvantages.

Choice depends on research questions, context, and expectedoutcomes.

Introduction to social network analysisNetwork metrics

Measuring properties of networks

Focus is on properties of patterns of relationships, independently ofnode attributes.

Based on the mathematics of graph theory, refined with socialscience concepts.

A variety of algorithms, measures and software applications areavailable.

Network size = number of nodes (= number of contacts in apersonal network);

The “Dunbar number”: cognitive limitations restrict the size ofpersonal networks to about 150 contacts;

An open question: have social media increased human capacity tomaintain relationships?

Median network size on Facebook = 99, average about 150 - 200(though large variation).

Density

The proportion of ties that actually exist and the ties that couldexist in principle:

Density = L(n∗(n−1))

2for undirected ties;

Density = L(n∗(n−1)) for directed ties.

where L = number of edges, n = number of nodes.

Density

Application: Dense networks and behaviours

Denser online networks spread behaviours faster: Centola 2010.

Density

Why is this so?

When adoption of a new behavior requires social reinforcement (threshold effect), a denser network favours change.

Centrality

Degree centrality

Who are the most “important” nodes?

Diane has the highest number of directconnections (degree);

A connector, or hub.

Krackhardt’s kite network.

Centrality

Degree centrality

Who are the most “important” nodes?

Diane has the highest number of directconnections (degree);

A connector, or hub.

Centrality

Betweenness centrality

Heather has fewer connections thanDiane;

Yet she occupies a strategic position,between different parts of the network;

She controls what flows in the network.

Centrality

Closeness centrality

Fernando and Garth have fewerconnections than Diane;

But they are at a shorter distance from allother network members;

They can monitor the information flow inthe network.

Centrality

Core-periphery structures

Ike and Jane have low centrality scores;

e.g. they may be external contractors fora company;

may be sources of fresh information!

Centrality

Network centralisation

The extent to which a network is dominated by one (or a few) nodes:

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Centrality

Network centralisation

Measures the extent to which a network is dominated by a singlecentral node.

Comparing centrality of the most central node to the centrality ofother nodes.

Normalized by dividing by the maximum centralization possible for anetwork of the given size.

Ranges from 0 to 1 (star network).

Centrality

Centralisation may vary over time

Figure: The advice network of judges in a Parisian court. Correlation between degrees, first to second observation(left panel) and second to third (right panel).

Distance

Distance: number of steps from one member to another;

Shorter paths in a network are the most important;

The shorter the path from one network to the other, the quickerand more efficient the flow of information, advice, knowledge.

Left: Longer paths; Right: Shorter paths.

Cliques

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3-member clique 4-member clique 5-member clique

A clique is a sub-set of nodes where all possible pairs of nodes aredirectly connected.Scott (2000).

Cliques

Real-world cliques

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1-clique 2-clique 3-clique

Completely connected groups uncommon.

n-clique: points connected by a maximum path link.

n-cliques of greater than 2 empirically infrequent.

Scott (2000).

Cliques

Application: Small Worlds

A “small world” network is sparse, but with dense neighbourhoods andshort paths; and there are few steps from one member to any other.

Cliques

Now you know:

Key metrics to measure properties of networks:

Density;

Centrality / Centralisation;

Distance;

Cliques.

Introduction to social network analysisFurther readings

Books on social network analysis: general

Thomas W. Valente. Social networks and health. Models, Methods,and Applications, Oxford UP 2010.

Christina Prell. Social Network Analysis. History, Theory andMethodology, Sage 2011 (October).

John P. Scott. Social Network Analysis: A Handbook, Sage 2000.

Books on social network analysis: general (cont.)

Stanley Wasserman and Katherine Faust. Social Network Analysis:Methods and Applications, Cambridge UP, 1994.

Peter J. Carrington, John Scott, Stanley Wasserman (Eds.) Modelsand Methods in Social Network Analysis, Cambridge UP, 2005.

David Knoke. Social Network Analysis, Sage 2008.

Books on social network analysis: Theory

Ronald S. Burt. Brokerage and Closure: An Introduction to SocialCapital, Oxford UP, 2005.

Ronald S. Burt. Neighbor Networks: Competitive Advantage Localand Personal, Oxford UP, 2010.

Nan Lin. Social Capital: A Theory of Social Structure and Action,Cambridge UP, 2002.

Books on social network analysis: Economics

Matthew O. Jackson Social and Economic Networks, Princeton UP,2010.

Sanjeev Goyal. Connections: An Introduction to the Economics ofNetworks, Princeton UP, 2009.

Fernando Vega-Redondo. Complex Social Networks,Cambridge UP2007.

Journals

Social Networks, Elsevier

Connections

Journal of Social Structure

Redes (Spanish)

Associations and conferences

INSNA: Sunbelt XXXIII conference, May 2013, Hamburg(www.insna.org);

AFS - RT26, Ecole d’été, September 2012;

UKSNA: 8th annual conference, Bristol, June 2012;

ASNA: 9th annual conference, Zurich, September 2012.

Thank you!

Paola Tubaro, p.tubaro@gre.ac.uk

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