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Introduction to Social Network AnalysisIntroduction to Social Network Analysis

Michela Ferron

SoNet group – Social Networking

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SummarySummary

Introduction to the Social Network perspectiveSome basic concepts of Social Network Analysis The main structural properties in Social Network

Analysis (some indices = formal measures)

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The Social Networks PerspectiveThe Social Networks Perspective

Recent decades:Recent decades: Social network and methods of SNA interest from social and behavioral science.SNA: focus on relationships among social entitiesThe social environment can be expressed asThe social environment can be expressed as patterns (regularities) in relationships among interacting units

Methods that are different from the traditionalMethods that are different from the traditional statistics and data analysis

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Social Network Analysis VSVS 

Traditional Research ApproachesppSNA as a distinct research perspective within the social and behavioral sciences:social and behavioral sciences:

Actors are viewed as interdependentActors are viewed as interdependentRelational ties are channels for transfer or “flow”

of resources (material and nonmaterial)of resources (material and nonmaterial)Structure as a set of lasting patterns of relations

among actorsamong actorsFocus on structure

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Unit of Analysis

“[…] the unit of analysis in network analysis is not the individual, but an entity consisting of a collection

of individuals and the linkages among them” (Wasserman & Faust 1994)(Wasserman & Faust, 1994)

Social network analysis is focused on uncoveringSocial network analysis is focused on uncovering the patterns of people's interaction.Assumption: how an individual lives depends inAssumption: how an individual lives depends in large part on how that individual is tied into the larger web of social connections.

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What is a Social Network? A definitionA definition

“A network is a set of interconnected nodes ” (Castells, 2001, p. 1)( , , p )

"[...] A social network is a set of people (or[...] A social network is a set of people (or organizations or other social entities) connected by a set of social relationships, such as friendship, co-working or information exchange“ (Garton et al., 2007)

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SNA Interdisciplinarity

A number of different disciplines contributed toA number of different disciplines contributed to the conceptualization of SNA, among which:

Formal MathematicsStatisticsStatisticsComputer ScienceSociology (Moreno)Sociology (Moreno)Anthropology (Barnes)P h lPsychology

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Basic example

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Fields of ApplicationsImpact of urbanization on well‐being

The world politic and economic system

Social support

Diffusion and adoption of innovationsp

Cognition and social perception

Community decision makingCommunity decision making

Organizational studies

Epidemiology studiesEpidemiology studies

Studies on terrorist networks

Telecommunication studiesTelecommunication studies

...

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Data collectionData collection

Questionnaire

InterviewInterview

Observation

Archival records

Experiments

...

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The concept of Relationf3 main characteristics of relations:

Content: the resource exchanged (material or not; i.e. in CMC contexts we can talk about the exchange of different kinds of information)

Direction:Directed relation: i.e. “support relations” giving support or receiving support

Undirected relation:  i.e. “to be married to someone”, “to be flatmates”

Strength: can be operationalized in a number g pof ways (i.e. pairs may communicate once a day, weekly or yearly)

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Network description

1 Set notation1. Set notation2. From the Graph Theory3 Matrix representation3. Matrix representation

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Network description

Examples (binary network = relations involve couples)

1. Set notation

A list of all the elements of a set of actors:X = {x₁, x₂, x₃, x₄},and a list of the pairs of elements which are linked by p ysome kind of social relationship

A = {(x₁, x₂), (x₂,x₁), (x₄,x₂), (x₃,x₂), (x₃,x₄), (x₄,x₃)}

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Network description (2)2. From the Graph theory

Actors are represented by points (nodes or vertex); )

Relations are represented by lines (edges) between two linked points

i.e. unvalued, directedh ( di h)graph (or di-graph):

for every relation we can identify a receivercan identify a receiverand a sender

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Network description (3)2. Matrix

In this example: a boolean (presence/absence p (pof a relation between couples of nodes, or diads), asimmetric matrix

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Why mathematics if we are talking about social concepts?about social concepts?

Linton FreemanLinton Freeman (Research Professor of Sociology at the University of California and founder of

the journal Social Networks):

“There are real problems when we try to reason in ordinay language [ ] as problems get more complicated theylanguage. […] as problems get more complicated, they

become harder to reason through. Our thinking gets fuzzy, and it’s difficult to tell wether the informal logic we use is, in

fact, logical. ” (Freeman, 1984, p. 345)

Mathematics is: formal concise abstractMathematics is: formal, concise, abstract, unambiguous.

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Main Structural Properties

Nodal degree

Density of a graph

Centrality measuresLocal and global centrality

(centralization)Degree centralityBetweenness centralityBetweenness centralityCloseness centrality

Reciprocity

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DegreeNodal Degree: number of lines incident with a node.

In directed graph:In directed graph:Nodal indegree: number of lines directed into a

node measure of RECEPTIVITY POPULARITYnode measure of RECEPTIVITY, POPULARITYNodal outdegree: number of lines directed from a

node to another one measure ofnode to another one measure of EXPANSIVENESS

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DensityDensity of a graph: proportion of possible lines that

are actually present in the graph (the ratio of theare actually present in the graph (the ratio of the number of the present lines to the maximum possible).

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Density

Density: general level of linkage among the pointsDensity: general level of linkage among the points measure of COHESION

CONSTRAINT: the larger the graph (other things being equal), the lower the density.g q ), y

Example: a graph of 5 actors will probably have a higher density than a graph of 5 hundred people

This limitation prevents density measures being f ffcompared across networks of different sizes.

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CentralityThe idea of centrality was one of the earliest in SNA.Centrality is one of the most studied proliferationCentrality is one of the most studied proliferation of formal measures, and thus sometimes, confusion.

Freeman (1979) talks of both:“point centrality” relative prominence of pointspoint centrality relative prominence of points

and “graph centrality” overall cohesion orand graph centrality overall cohesion or integration of the graph

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Local centrality based on nodal degreedegree

Nodal degree: a measure of centrality (it showsNodal degree: a measure of centrality (it shows how well connected the point are within their local environment)BUT: nodal degree depends on the group size

constraints for comparisonsp

Degree centralityg y

An actor has a high degree centrality if he/she is very active has many ties to other actors.Prominence = “activity” or “degree”

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Local centrality based on betweenness

Betweenness centrality: Interactions between two

betweennessBetweenness centrality: Interactions between two nonadjacent actors might depend on other actors, who might have some control over the interactions of the others.

An actor has a high betweenness centrality if he/she lies between many of other actors (technically, on their geodesic)Prominence = “control on communication”

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Local centrality of a node (3)

Closeness centrality: focuses on how close anCloseness centrality: focuses on how close an actor is to all the others in the network.

An actor has a high closeness centrality if he/she can quickly interact with all others. q y

In a communication context, he/she doesn’t need ,to rely on other actors for the relaying of information (short communication paths to the others)Prominence = “independence” or “efficiency”

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Global centrality or centralization

For every measure of local centrality there is aFor every measure of local centrality there is a corresponding measure of global centrality, or “centralization”: These measures quantify the variability(dispersion, range) of the individual actor indices.

In general, Degree, Betweenness, and Closeness centralization grow as theCloseness centralization grow as the network become less homogeneous and thus more centralized i.e. they are maximum in the sociometric star

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Reciprocity

Fundamental question: how strong is theFundamental question: how strong is the tendency for one actor to choose another one, if the second actor chooses the first?

Reciprocity is an index of mutuality, it shows the p y ytendency to reciprocate choices more frequently than by chance.

It’s more that a descriptive measure: it’s based on the expectation of the number of mutual dyads.

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Thank you.y

…

Questions?

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References and Resources

Castells, M. (2001). The Internet Galaxy. New York: Oxford University Press Inc.

Freeman, L. C. (1979). Centrality in social networks: Conceptual clarification Social Networks 1 215-239Conceptual clarification. Social Networks, 1, 215-239.

Freeman, L. C. (1984). Turning a profit from mathematics: The case of social networks. Journal of Mathematical Sociology, 10, 343-360.

Garton, L., Haythornthwaite, C., & Wellman, B. (1997). Studying online social networks Journal of ComputerStudying online social networks. Journal of Computer-Mediated Communication, 3(1). Retrieved November, 7th, 2008 from http://jcmc.indiana.edu/vol3/issue1/garton.html.

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References and Resources (2)

Katz, L., & Powell, J. H. (1955). Measurement of the tendency toward reciprocation of choice. Sociometry, 18(4), 403-409.

Wasserman, S., & Faust, K. (1994). Social network analysis. Methods and applications. Cambridge, MA: C b id U i it PCambridge University Press.

Wellman, B. (1997). An electronic group is virtually a social network. In S. Kiesler (Ed.), Culture of the Internet (pp. 179-( ), (pp205). Mahwah, NJ: Lawrence Erlbaum Associates.