A brief introduction to the social network perspective and to some basic concepts in social network analysis

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Introduction to Social Network Analysis
Michela Ferron
SoNet group – Social Networking
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Summary
Introduction to the Social Network perspective
Some 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 Perspective
The Social Networks Perspective
Recent decades:
Social network and methods of SNA interest
from social and behavioral science.
SNA: focus on relationships among social entities
The social environment can be expressed as
patterns (regularities) in relationships among
interacting units
Methods that are different from the traditional
statistics and data analysis
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Social Network Analysis
VS
VS
Traditional Research Approaches
pp
SNA as a distinct research perspective within the
social and behavioral sciences:
Actors are viewed as interdependent
Relational ties are channels for transfer or “flow”
of resources (material and nonmaterial)
Structure as a set of lasting patterns of relations
among actors
Focus 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)
Faust
Social network analysis is focused on uncovering
the patterns of people's interaction.
Assumption: 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 definition
A definition
“A network is a set of interconnected nodes ”
(Castells, 2001, p. 1)
( , ,p )
quot;[...] 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 to
the conceptualization of SNA, among which:
Formal Mathematics
Statistics
Computer Science
Sociology (Moreno)
Anthropology (Barnes)
Psychology
P h l
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Basic example
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Fields of Applications
Impact of urbanization on well‐being
The world politic and economic system
Social support
Diffusion and adoption of innovations
p
Cognition and social perception
Community decision making
Community decision making
Organizational studies
Epidemiology studies
Epidemiology studies
Studies on terrorist networks
Telecommunication studies
Telecommunication studies
...
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Data collection
Data collection
Questionnaire
Interview
Observation
Archival records
Experiments
...
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The concept of Relation
3 main characteristics of relations:
f
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 p
of ways (i.e. pairs may communicate once a day,
weekly or yearly)
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Network description
1.
1 Set notation
2. From the Graph Theory
3.
3 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 y
some 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, directed
graph ( di
h (or di-graph):
h)
for every relation we
can identify a receiver
and a sender
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Network description (3)
2. Matrix
In this example: a boolean (presence/absence
p (p
of 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 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, they
language. [ ] complicated
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, abstract,
formal concise abstract
unambiguous.
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Main Structural Properties
Nodal degree
Density of a graph
Centrality measures
Local and global centrality
(centralization)
Degree centrality
Betweenness centrality
Closeness centrality
Reciprocity
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Degree
Nodal Degree: number of lines incident with a node.
In directed graph:
Nodal indegree: number of lines directed into a
node measure of RECEPTIVITY POPULARITY
RECEPTIVITY,
Nodal outdegree: number of lines directed from a
node to another one measure of
EXPANSIVENESS
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Density
Density of a graph: proportion of possible lines that
are 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 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
compared across networks of different sizes.
f ff
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Centrality
The idea of centrality was one of the earliest in SNA.
Centrality is one of the most studied proliferation
of formal measures, and thus sometimes, confusion.
Freeman (1979) talks of both:
“point centrality”
point centrality relative prominence of points
and “graph centrality”
graph centrality overall cohesion or
integration of the graph
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Local centrality based on nodal
degree
Nodal 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 comparisons
p
Degree centrality
g 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
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 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 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 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 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 y
tendency 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 1 215-239
clarification 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 Computer
networks 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
Cambridge University P
it Press.
Wellman, B. (1997). An electronic group is virtually a social
network. In S. Kiesler (Ed.), Culture of the Internet (pp. 179-
( ), (pp
205). Mahwah, NJ: Lawrence Erlbaum Associates.
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