"Introduction in Social Network
Analysis. Theoretical Approaches and
Empirical Analysis with computerassisted programmes."
Dr. Denis Gruber
State University of St. Petersburg
Faculty of Sociology
DAAD-Lecturer for Sociology
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Networks and Power:
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Chris
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Who has more Power?
What is a network?
Definition:
„(...) a specific set of linkages among a defined set of persons with the additional
property that the characteristics of these linkages as a whole may be used to
interpret the social behavior of the persons involved.“ (Mitchell 1969:2)
What is Social Network Analysis?
• “(…) is based on an assumption of the importance of relationships among
interacting units“ (Wasserman/Faust 2008:4)
• “(…) encompasses theories, models, and applications that are expressed in
terms of relational concepts or processes” (Wasserman/Faust 2008:4)
• “(…) 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 2008:5)
Network methods focus on:
• Dyads (two actors and their ties)
• Triads (three actors and their ties)
• Larger systems (subgroups of individuals, or entire networks)
Primary literature:
Wasserman, Stanley / Faust, Katherine (2008): Social Network Analysis.
Methods and Applications, Cambridge, University Press
Principles of Social Network Analysis
• Actors and their actions are viewed as interdependent rather than
independent, autonomous units
• Relational ties (linkages) between actors are channels for transfer or
“flow” of resources (either material or nonmaterial)
• Network models focusing on individuals view the network structure
environment as providing opportunities for or constraints on individual
action
• Network models conceptualize structure (social, economic, political, and
so forth) as lasting patterns of relations among actors
(Wasserman/Faust 2008:4)
The Social Network Approach
• The world is composed of networks
- not densely-knit, tightly-bounded groups
• Networks provide flexible means of social
organization and of thinking about social
organization
• Networks have emergent properties of structure and
composition
• Networks are a major source of social capital
• Networks are self-shaping and reflexive
• Networks scale up to networks of networks
Overview about the development of
Social Network Analsis
1930
1950/60
1970
(Scott 1991, 7)
Persönlichen Netzwerke und Gesamtnetzwerke
Bei der Untersuchung von Gesamtnetzwerken ermittelt man nun zu
jedem Akteur, ob Beziehungen zu jedem anderen Akteur der Menge
bestehen oder nicht.
Bei den persönlichen Netzwerken hingegen stellt man für jeden Akteur
fest, mit welchen Akteuren Beziehungen der vorgegebenen Art
bestehen.
Gesamtnetzwerk:
A7
Persönliche Netzwerke:
A7
A6
A6
A2
A2
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Which differences exist between a social network analysis and
a non-network explanation?
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in non-network explanations the main focus is on: attributes of autonomous
individual units, the associations among these attributes, and the usefulness of
one or more attributes for predicting the level of another attribute
social network analysis:
refers to the set of actors and the ties among them
views on characteristics of the social units arising out of structural or relational
processes or focuses on properties of the relational system themselves
inclusion of concepts and information on relationships among units in a study
the task is to understand properties of the social (economic or political) structural
environment, and
how these structural properties influence observed characteristics and
associations among characteristics
relational ties among actors are primary and attributes of actors are secondary
each individual has ties to other individuals, each of whom in turn is tied to a few,
some, or many others, and so on
(Wasserman/Faust 2008: 6-9)
What is a Social Network?
• A set of nodes (e.g., people or organisations)
• A set of connections between nodes (e.g.,
friends, acquaintances, relatives)
Social network analysis is often
interested in paths or chains
communicating information
Fundamental Concepts in Network
Analysis
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actor
relational tie
dyad
triad
subgroup
group
relation
social network
Actor
• “discrete individual, corporate, or collective social units”
(Wasserman/Faust 2008:17)
• Examples: people in a group, departments within in a corporation, public
service agency in a city, nation-states in the world system
• Does not imply that they have volition or the ability to “act”
Relational tie
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Actors are linked to another by social ties
A tie “establishes a linkage between a pair of actors”
Example of ties in SNA (Wasserman/Faust 2008:17):
Evaluation of one person by another (expressed friendship, linking, or
respect)
Transfers of material resources (business transactions, lending or
borrowing things)
Association or affiliation (jointly attending a social event, or belonging to
the same social club)
Behavioral interaction (talking together, sending messages)
Movement between places or statuses (migration, social or physical
mobility)
Physical connection (a road, river, or bridge connecting two points)
Formal relations (authority)
Biological relationships (kinship or descent)
Dyad
• a tie between two actors
• “consists of a pair of actors and the (possible) tie(s) between them”
(Wasserman/Faust 2008:18)
• Shows “properties of pairwise relationships, such as whether ties are
reciprocated or not, or whether specific types of multiple relationships
tend to occur together” (Wasserman/Faust 2008:18)
Triad
• “Triples of actors and associated ties” (Wasserman/Faust 2008:19)
• “a subset of three actors and the (possible) tie(s) among them”
(Wasserman/Faust 2008:19)
• Triadic analyses focus on the fact whether the triad is
• Transitive : if actor i “likes” actor j, and actor j in turn “likes” actor k, then
actor i will also “like” actor k
• Balanced: if actors i and j like each other, then i and j should be similar in
their evaluation of a third actor, k, and i and j dislike each other, then they
should differ in their evaluation of third actor, k
Subgroup
• Subgroup of actors is defined “as any subset of actors, and all ties among
them” (Wasserman/Faust 2008:19)
Group
• “is the collection of all actors on which ties are to be measured”
(Wasserman/Faust 2008:19)
• Actors in a group “belong together in a more or less bounded set (…)
consists of a finite set of individuals on which network measurements are
made” (Wasserman/Faust 2008:19)
• “The restriction to a finite set or sets of actors is an analytic requirement.
Though one could conceive of ties extending among actors in a nearly
infinite group of acts, one would have great difficulty analyzing data such a
network. Modeling finite groups presents some of the more problematic
issues in network analysis, including the specification of network
boundaries, sampling, and the definition of group. Network sampling and
boundary specification are important issues.” (Wasserman/Faust
2008:19f.)
• “however, in research applications we are usually forced to look at finite
collections of actors and ties between them.” (Wasserman/Faust 2008:20)
Relation
• “the collection of ties of a specific kind among members of a group”
(Wasserman/Faust 2008:20)
• Example: the set of friendship among pairs of children in a classroom
• For group of actors, several different relations might be measured
• “refers to the collection of ties of a given kind measured on pairs of actors
from a specified actor set” (Wasserman/Faust 2008:20)
• Ties themselves only exist between specific pairs of actors
Social network
• “consists of a finite set or sets of actors and the relation or relations
defined on them. The presence of relational information is a critical and
defining feature of a social network.” (Wasserman/Faust 2008:20)
• “A social network arises when all actors can, theoretically, have ties to all
relevant actors” (Wasserman/Faust 2008:42)
Work data sets
• What are network data?
• Boundary specification and
sampling
• Types of networks
What are network data?
• variables
• modes
• affiliation variables
Variables
(Wasserman/Faust 2008:29)
• structural variables:
 are measured on pairs of actors and are the cornerstone of social network
data sets
 measure ties of a specific kind between pairs of actors
 example: business transaction between corporations, friendship between
people, trade between nations
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composition variables:
measurements of actor attributes (actor attribute variables)
are of the standard social and behavioral science variety
defined at the level of individual actors
example: gender, race, ethnicity for people
Modes
• “the number of sets of entities on which structural variables are
measured” (Wasserman/Faust 2008:35)
• One-mode network: all actors come from one set
• two-mode network: there are two set of actors: e.g. set consisting of
corporations and another of non-profit organizations, contains
measurements on which actors from one set have ties to actors from the
other set
• higher-mode network: more set of entities: actors from different sets
Affiliation Variables
• each affiliation variable is defined on a specific subset of actors
• a special type of two-mode network, but they only have one set of actors
• the second mode is a set of events: such as clubs or voluntary
organizations to which the actor belong
• “events are defined not on pairs of actors, but on subsets of actors (…)
often events are informal social occasions, such as parties or other
gatherings, and observations or attendance or interactions among people
provide the affiliation of the actors ”
• “subsets can be of any size”
Boundary specification and sampling I
What is your Population? (Wasserman/Faust 2008:31)
• Who are the relevant actors?
• Example: faculty in an academic department or corporations
headquartered in a major metropolitan area: relatively easy to deal with
• But what to do in other cases if the boundary of the set of actors may be
difficult if not impossible to determine
• “The boundary of a set of actors allows a researcher to describe and
identify the population under study”
• Actor set boundaries are often based on the relative frequency of
interaction, or intensity of ties among members as contrasted with nonmembers
Boundary specification and sampling II
• Two different approaches to boundary specification in social network
studies (cf. Laumann, Marsden, Prensk 1989)
• Realist approach: focuses on actor set boundaries and membership as
perceived by the actors themselves (e.g. a street gang, members
acknowledge as belonging to the gang)
• Nominalist approach: based on the theoretical concerns of the researcher
(e.g. flow of computer messages among researchers in a scientific
community; the list of actors might be the collection of people who
published papers on the topic in the previous five years)
• In several applications, when the boundary is unknown, special sampling
techniques such as snowball sampling and random nets
(Wasserman/Faust 2008:32)
Boundary specification and sampling III: Sampling
• sometimes it is not possible to take measurements on all actors in the
relevant actor set (Wasserman/Faust 2008:33)
• is seen as “representative of the larger, theoretically interesting
population (which must have a well-defined boundary and hence, a
known size), and uses the sampled actors and data to make inferences
about the population)
• example:
• snowball network sample (cf. Goodman 1961): “begins when the actors in
a set of sample respondents report on the actors to whom they have ties
of a specific kind” (Wasserman/Faust 2008:34)
• all of the nominated actors constitute the “first order “ zone of the
network
• then all actors in this zone will be sampled and all the additional actors
(those nominated by the actors in the “first order” zone who are not
among the original respondents or those in this zone) are gathered
• these additional actors constitute the “second order” zone
• it is a chain method what means that several “order zones” can be defined
"Introduction in Social Network Analysis.
Theoretical Approaches and Empirical
Analysis with computer-assisted
programmes."
II. meeting:
- Types of networks for SNA
- From organic solidarity (Durkheim) to
information society and network society
(Castells)
- Social capital and social networks
- Quiz
Social Network Analysis:
Focus on interactions between individuals/ groups
Node: Any entity in
a network
(person, system,
group, organization)
Tie: Relationship/
interaction
between two nodes.
Sociology of networks
beware – network analysis takes very distinct forms!
sociometry
Moreno (psychotherapy)
graph theory
White (mathematical sociology)
social capital
Bourdieu (social theory)
networks
‘strength of weak ties’
Granovetter (new ec sociology)
social exclusion
Phillipson (social policy)
network culture
network society
Castells (social theory)
Terranova (cultural studies)
Types of networks
• Network can be categorized by the nature of the sets
of actors and the properties of the ties among them
• “The number of modes in a network refers to the
number of distinct kinds of social entities in the
network” (Wasserman/Faust 2008:35)
One-mode networks: a single set of actors
Two-mode networks: focus on two sets of actors, or
one set of actors and one set of events
One-mode networks: a single set of actors
(Wasserman/Faust 2008:36f.)
What is important inside?
• actors
• relations
• actor attributes
Actors in one-mode networks
can be a variety of types
 People
 Subgroups (consist of people
 Organizations
 Collectives / Aggregates: Communities
(consists of subgroups of people), nationstates (larger entities, containing many
organizations and subgroups)
Relations in one-mode networks
(Wasserman/Faust 2008:37)
 individual evaluations: friendship, linking, respect  “measurements of
positive or negative affect of one person for another”
 transactions or transfer of material resources: lending or borrowing; buying or
selling, contacts made by one actor of another in order to secure valuable
resources, transfer of goods, social support ties
 transfer of non-material resources: communications, sending/receiving
information  frequently communications between actors, where ties
represent messages transmitted or information received
 interactions: physical interaction of actors or their presence in the same place
at the same time, e.g. sitting next to each other, attending the same party,
visiting a person’s home
 movement: physical (migration from place-to-place), social (movement
between occupations or statuses)
 formal roles: e.g. dictated by power and authority in a management setting
 kinship: marriage, descent
Actor Attributes
People can be queried about different features,
like
age
gender
race
socioeconomic status
place of residence
grade in school, etc.
Two Sets of Actors
 focus on two sets of actors, or one set of actors and
one set of events
• Relations measure ties between the actors in one set
and actors in a second set
• Described as dyadic two-mode networks, because
actors from the first set are different from the actors
of the second set
Wasserman/Faust 2008:39
Manuel Castells’
theory of The
Network Society
What is a Network Society?
• A new techno-economic system (society) where the key social
structures and activities are organized around electronically
processes information networks
Social Structures:
• involve the organized arrangements of humans in relations of
production, consumption and reproduction,
• experiences and power expressed in meaningful
communication coded by culture
Networks:
- a set of interconnected nodes, with no centre
- networks have been very old forms of social organization
- It is about social networks which process and manage
information and are using micro-electronic based
technologies
What is a Network Society?
• Social integration/impact
– The demise of Mass audiences
– Two-way communication and interactivity
– The death of time and distance
– Personalized media
– Globalization and Cultural standardization
• Transformations in Politics and democracy (see virtual political
parties, e-voting, e-referenda, e-advocacy, e-news etc)
• Transformation of work and employment
Castells calls three main trends for
the rise of a network society
- The process of transformation to a network society
started in the 1970s through the interaction of three
independent trends:
•the invention of microelectronics and the IT
revolution
•the crisis of industrialism in both capitalist and statist
societies,
•the profound cultural challenge mounted by the rise
of social movements in the late 1960s
Castells, M. (1991), The Informational City. Information Technologies, Economic
Restructuring, and the Urban-Regional Process, Oxford and Cambridge, Basil
Blackwell
• network society is a social order embodying a logic
like ‘space of flows’
• space of flows is the material organization of timesharing social practices that work through flows
• flows are purposeful, repetitive, programmable
sequences of exchange and interaction between
physically disjointed positions held by social actors
in the economic, political, and symbolic structures
of society
• presence and absence are critical sources of
domination and change in our society
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Castells, M. (1991), The Informational City
• New information technologies are
integrating the world in global networks of
instrumentality
• In the new, informational mode of
development the source of productivity lies
in the technology of knowledge generation,
information processing, and symbol
communication
• the action of knowledge is the main source
of productivity
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On social capital
• scholars do not agree whether it refers to ‘resources’ or
networks or a combination of social structure and
networks and ideas and values associated with them
• Following Foley and Edwards (2001) who reviewed the
literature found that the term is mainly used to refer to
associational life or social networks and not to social
norms as such
• Four important sociologists, however, focus on actorcentered and network-related social capital as a
valuable resource: Pierre Bourdieu, James Coleman,
Robert Putnam and Francis Fukuyama
Pierre Bourdieu
• considers social capital of an actor as an exploitation of a
permanent net of more or less institutionalized relations of
mutual knowledge and recognition
• considers social capital as a resource among other capital
forms (economic capital, cultural capital, symbolic capital)
• Social capital is based upon membership to a group
- The larger social net of personal relations
- which he can take reference to
- higher profit chances in the reproduction of his economic and
cultural capital
James Coleman
• Social capital is a variety of different entities, with
two elements in common: “They all consist of some
aspect of social structures, and they facilitate certain
actions of actors - whether persons or corporate
actors - within the structure.”
• unlike other forms of capital, social capital inheres in
the structure of relations between actors and among
actors
Coleman 1988: 98
Network Analysis and Social Capital
-Social capital can be understood under a network
theoretical approach as an aspect of the social
structure which enlarges or restricts individual or
corporative actions
- in opposite to economic and human capital, social
capital is not only restricted to the single actor but to
his relations to other actors and their positions within
the network
- other actors who are not directly linked with the
focussed actor are able to influence the situation
indirectly
Network Analysis and Social Capital
- Its hinge function between actors (individuals,
collectivs, corporates) Körperschaften) and social
structure offers the focus on following fields of interest:
(1) Question about social capital of a single actor within
a network and ist possibilities of strategial influence
(2) Question about how different actors can be
compared with regard to their positions within the
network
(3) Question which influence does social capital have
onto the network as well as onto the whole society
network-theoretical considerations I
• Granovetter’s (1977) linkage of network morphology with action, by
considering strong and weak network ties
• Among strong relations there is the tendency of cluster formation, whereas a
linkage between different clusters can only occur by weak ties that form
bridges between these
• The ‘Strength of Weak Ties’ (the title of this article) is therefore their ability to
open up closed networks
• Weak ties: more of them with unconnected others, better for finding jobs
• Strong ties: less of them with related others, better for trust
• Recent approaches that apply Granovetter’s distinction to the notion of social
capital, distinguish ‘bonding capital’ (between people) and ‘bridging capital’
(between groups).
Social Network Theories
• Strong ties
– Trust that exchange partners will not act in selfinterest at expense of others
– Creates ideal conditions for:
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Knowledge diffusion
Collaborative problem solving
Climate of informal governance
Optimization of member contributions
(Levin and Cross, 2004)
Social Network Theories
• Strength of weak ties Networks based on
weak ties (distant and infrequent
relationships) are more efficient at sharing
knowledge as they provide access to novel
information from otherwise disconnected
parties
– Less “dense” networks:
• Reduce redundancy of information/resources
• Increase diversity of resources
(Granovetter , 1982)
Francis Fukuyama
• considers social capital as an important factor for welfare and
competitiveness of a nation
• social capital is a given set of informal norms and values, which all
members of a group share, and which facilitate cooperation
between the group members
• When these assume that others will behave in a trustful and
reliable way, they will trust each other (Fukuyama 1992: 32)
• the ability and capacity to communicate in an uncomplicated way
and to cooperate is a ‘spontaneous solidarity’, which constitutes an
important part of social capital
• It plays an important role in the creation and maintenance of civil
society, because spontaneous sociability enables people, who do
not know each other, to congregate and cooperate with each other
Alena Ledeneva : The Concept of Blat. The Network Economy in
Post-Soviet Russia
• defines blat “as an exchange of ‘favours of access’ to
public resources in conditions of shortages and a
state system of privileges” (Ledeneva, 1998:37)
• Through blat networks public resources were
redirected to private uses and to the needs of
personal consumption
• These relations were often disguised by the rhetoric
of friendship, such as ‘helping out’ a friend or an
acquaintance
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Alena Ledeneva : The Concept of Blat. The Network Economy in
Post-Soviet Russia
• sees blat networks as both vital to the Soviet social order and subversive
of it
• They were needed in most aspects of daily life in the Soviet Union such as
obtaining foodstuffs, train tickets, medical services, study places at
university or specialized schools, jobs, cars, and apartments
• Most of the restrictions and harshness of everyday life could in fact be
avoided by blat
• distinguishes blat from apparently similar phenomena, e.g. clientelism and
other corrupt practices, by being less morally doubtful and therefore more
pervasive
• blat was based on personal relations implying continuity of the
relationship and was often disguised as friendly help
• blat was only conceivable in the context of socialist shortage economy and
the state-governed system of distribution.
Alena Ledeneva : The Concept of Blat. The Network Economy in
Post-Soviet Russia
• the role of networks is clearly present in the
studies of the “second”, “shadow” or
”informal” economy of the Soviet Union, postSoviet Russia, SU-successor states and Eastern
Europe
• But what happened to these networks with
the collapse of communism?
• Are they still viable in post-socialist society?
Alena Ledeneva : The Concept of Blat. The Network
Economy in Post-Soviet Russia
• Ledeneva argues that the network economy is
inherited from the Russian/Soviet past and carries
features inhibiting democratic development
• The relationship between formal institutions and
informal networks is more complicated than that
• argument: the fundamental principle of the network
economy, however, has not change, but following
political, economic and social changes, informal networks
started modifying and filling in available and newly
created loopholes.
"Introduction in Social Network Analysis.
Theoretical Approaches and Empirical Analysis
with computer-assisted programmes."
V. meeting:
- Introduction in the computer programme „UCINET“
UCINET--Introduction
• UCINET—UCINET is produced by Analytic
Technologies. It offers a very user-friendly,
reasonably priced software system for
network analysis.
• Throughout this discussion, we’ll use the
example of the cosponsorship network of the
58 legislators in the lower house of the
Arizona legislature, 2001.
Starting UCINET
• When you first open UCINET, set the default directory to a
directory of your choice, by typing in the directory name (into
the space at the bottom edge of the UCINET window). Note
that the original default directory is just the c:\ drive.
• Note that UCINET produces many types of files—and deleting
any (before you are entirely done with your analysis) may
make it difficult to use some of the others.
QAP Procedure
• UCINET also allows the possibility of a
regression analysis, using a QAP procedure.
• The QAP Procedure will be the focus of our
next discussion.
UCINET--Introduction
• offers a very user-friendly, reasonably priced
software system for network analysis
• Throughout this discussion, we’ll use the
example of the cosponsorship network of the
58 legislators in the lower house of the
Arizona legislature, 2001.
Starting UCINET
• When you first open UCINET, set the default
directory to a directory of your choice, by typing in
the directory name (into the space at the bottom
edge of the UCINET window). Note that the original
default directory is just the c:\ drive.
• Note that UCINET produces many types of files—and
deleting any (before you are entirely done with your
analysis) may make it difficult to use some of the
others.
How to Read Data into UCINET
• There are several ways to read network data into UCINET.
I’ll review two basic methodsusing matrices, and using dl
language.
• UCINET can read in a matrix data—either saved in a text
file, or saved in excel.
• So, in the case of the Arizona cosponsorship data that we
will use as an example, there are 58 legislators – and
therefore 58 X 58 = 3,364 dyads.
Please paint a sociogram!
Matrix
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
Please find a matrix!
Bob
Carol
Ted
Alice
1
2
3
4
Susan 1
Kathy 2
Tanya 3
Donna 4
Nancy 5
Manuel 6
Charles 7
Harold 8
Carol
9
Stuart 10
Fred 11
Bob
12
Sharon 13
Wynn 14
Please find a matrix!
B
A
D
C
E
I
G
H
F
M
K
J
L
various questions can be answered
•
•
•
•
Which player initiated the most passes (Jazic)?
Who was on the receiving end of the most passes (Jazic)?
Who controlled Rapid’s play (Jazic, Hoffman)?
Which players were involved in the most combination pass plays (Jazic,
Hofmann, Feldhofer, Martinez, Carics)?
• Who played together with whom and
who didn’t (not a single pass from Ivanschitz
to Wagner!)?
• Which combinations of players made up
the backbone of the team
(e.g. the Feldhofer-Carics-Pashazadeh triad)?
• Which players had a similar role
(Ivanschitz / Martinez)?
Please find a matrix!
Robinson
1
Cole Ashley 2
Terry
3
Ferdinand 4
Neville
5
Cole Joe
6
Lampard
7
Heargraves 8
Gerrard
9
Beckham 10
Lennon
11
Crouch
12
Rooney
13
Which player
initiated the most
passes?
Who was on the
receiving end of
the most passes?
Who has controlled
England’s play?
Which players did
not play together?
Which players had
a similar role?
SNA – linkage between Visualization and Data
• Graph theory is universally applicable in
modeling social relationships
• Data on social relationships are transformed
into graphs and evaluated on different
analytical levels
• levels base on the individual agent, dyadic or
triadic level, cluster level, level of the entire
network
c.f. Katzmeier (2007): Social Network Analysis. The Science of Measuring, Visualizing and Simulating
Data on Social Relationships, Working Paper Series, Vienna
Typical Social Relationships for Network
Analytical Consideration:
c.f. Katzmeier (2007): Social Network Analysis. The Science of Measuring, Visualizing and Simulating
Data on Social Relationships, Working Paper Series, Vienna
Software for Social Network Analysis
Huisman, van Duijn (2003): Software for Social Network Analysis, University of Groningen, Working Paper Series, p.3
"Introduction in Social Network Analysis.
Theoretical Approaches and Empirical Analysis
with computer-assisted programmes."
IV. meeting:
- Short overview about computer programme „Pajek“
- Introduction in the computer programme „VISONE“
Social Network Analysis
Pajek
What is Pajek
–Pajek is a program, for Windows, for analysis of large networks.
–Authors:
–Andrej Mrvar, Faculty of Social Sciences, University of Ljubljana.
–Vladimir Batagelj, Faculty of Applied Mathematics, University of
Ljubljana.
–Pajek started to develop in November 1996.
–Pajek is freely available, for noncommercial use, at its homepage
Pajek
• Pajek (Version 0.94; Batagelj and Mrvar, 2003a) is a
network analysis and visualization program, specially
designed to handle large data sets
• main goals in the design of Pajek are:
1) to facilitate the reduction of a large network into
several smaller networks that can be treated further
using more sophisticated methods
2) to provide the user with powerful visualization tools,
and
3) to implement a selection of efficient network
algorithms (Batagelj and Mrvar, 1998)
With Pajek we can find
• clusters (components, neighborhoods of
‘important vertices, cores, etc.) in a network
• extract vertices that belong to the same
clusters and show them separately, possibly
with the parts of the context (detailed local
view)
• shrink vertices in clusters and show relations
among clusters (global view)
Pajek (Slovene word for Spider)
Pajek
Pajek uses six different data structures:
1) networks (nodes and arcs/edges),
2) partitions (classifications of nodes, where each node
is assigned exclusively to one class),
3) permutations (reordering of nodes)
4) clusters (subsets of nodes),
5) hierarchies (hierarchically ordered clusters and
nodes), and
6) vectors (properties of nodes)
Social Network Analysis
Visone
Basic Literature
• Baur, Michael (2008): Visone. Software for the
Analysis and Visualization of Social Networks,
in:
http://digbib.ubka.unikarlsruhe.de/volltexte/1000010897
Visone
• a tool that facilitates the visual exploration of social networks
• an attempt to integrate analysis and visualization of social
networks
• origins of Visone lie in an interdisciplinary cooperation with
researchers from political science which
• resulted in innovative uses of graph drawing methods for
social network visualization, and prototypical
implementations thereof
• In a nutshell, Visone is a
- tool for interactive analysis and visualization of networks, in
which
- originality is preferred over comprehensiveness, and that
- caters especially to social scientists.
Model
• A social network consists of nodes (often referred to
as actors), i.e. entities such as persons, organizations
• simply objects that are linked by binary relations
such as social relations, dependencies, or exchange
• Both nodes and links may have additional attributes
• Relations constituting a social network may be
directed, undirected, or mixed
• Attributes can be of any type, and numerical link
attributes may strengthen or weaken the tie
between two nodes
Analysis
• purpose of social network analysis is to identify important
actors, crucial links, roles, dense groups, and so on, in order to
answer substantive questions about structure
• analysis methods available in visone are divided into four
main categories according to the level or subject of interest:
vertex, dyad, group, and network level
• available analysis methods include actor-level centrality
indices, e.g. closeness, betweenness, and pagerank, cohesive
subgroups like cliques, k-cliques, and k-clans, centrality and
connectedness
• These levels break further down into measures of the same
objective, e. g., connectedness or cohesiveness
• analysis methods are accessible using the analysis tab in the
control area
Analysis
• The purpose of social network analysis is to identify important
actors, crucial links, subgroups, roles, network characteristics,
and so on, to answer substantive questions about structures
• There are three main levels of interest: the element, group,
and network level
• On the element level: one is interested in properties (both
absolute and relative) of single actors, links, or incidences, e.g.
structural ranking of network items
• On the group level: one is interested in classifying the
elements of a network and properties of sub-networks, e.g.
actor equivalence classes and cluster identification
• On the network level: one is interested in properties of the
overall network such as connectivity or balance
Confirmation
• also called reciprocity
• Unconfirmed edges emerge for example when two
actors have divergent perceptions of the existence or
specificity of their relation or when one of them
simply lies
• Such unconfirmed connections exhibit an additional
form of direction induced by the actor who test ties
for it
• a directed edge is called sender confirmed if it is
confirmed by its tail and receiver confirmed if it is
confirmed by the head
Characteristics of Input Data
• Direction
• Edge Weights
• Multi-Edges
• Loops
Direction
• Typically, a formulation of an algorithm allowing directed edges is
more general than one for undirected edges since for almost all
purposes
• each undirected edge fu; vgis replaced equivalently by two
symmetric, contrariously directed edges (u; v) and (v; u)
• one. In particular, two symmetric, contrariously directed edges (u;
v) and (v; u) are replaced by two undirected edges fu; vg which may
be unintentional
Edge Weights
Are depending on the context:
strength (larger is better) or
length (smaller is better)
- for each method, it is clearly labeled if a
weight is considered as strength or as length
- For some methods, even two weights of
dierent meaning can be specied
- However, it is the user's responsibility to
select a reasonable attribute as weight
Weights and Attributes
• one is not only interested in the existence of
edges but in a quantication of the
interconnections
• this may be the frequency of meetings, the
helpfulness of advice, or the costs of exchange
The main use cases of attributes are:
• store user data, e. g., weights and semantical
element information,
• specify input parameters of analyses methods,
typically as edge weights,
• store the result of analyses methods, e. g., centrality
indices, a partitioning, or
• clique membership, and
• specify input parameters of visualizations, e. g., the
index or the partitioning
• to depict in a drawing.
Visualization
•
1.
2.
there are two obvious criteria for the quality of social
network visualizations:
the information manifest in the network represented
accurately?
Is this information conveyed efficiently?
•
the following three aspects should be carefully thought
through when creating network visualizations:
-
the substantive aspect the viewer is interested in,
the design (i.e. the mapping of data to graphical variables),
and
the algorithm employed to realize the design (artifacts,
effciency, etc.)
-
Introduction in Social Network
Analysis
Exercise 1
• People that participate in social events
• Incidence matrix:
A
B
C
D
E
1
1
1
1
1
0
2
1
1
1
0
1
3
0
1
1
1
0
4
0
0
1
0
1
Exercise 2
• Matrices
Ann
Rob
Sue
Nick
• Graphs?
Ann Rob Sue Nick
--1
0
0
1
--1
0
1
1
--1
0
0
1
---
Exercise 3
0:E
1:M
Matrix?
2:B
3:L
4:P
Exercise 3
0 1 2 3 4
Adjacency
matrix
0
1
2
3
4
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
Exercise 4
Exercise 5
Build a socio-matrix
From pictures to matrices
b
b
d
a
c
e
a
c
Undirected, binary
a
b
c
d
d
e
Directed, binary
e
a
a
b
a
b
c
c
d
e
d
e
b
c
d
e
Build a socio-matrix
Exercise 5
From pictures to matrices
b
b
d
a
c
e
Undirected, binary
a
b
1
a
b 1
c
1
d
e
c
d
1
1
c
e
a
1
a
b 1
c
1
d
e
1
1
a
e
Directed, binary
1
1
d
b
1
c
1
d
e
1
1
1
Social Network Properties
• Centrality and Power
Degree
• Number of links that a node has
• It corresponds to the local centrality in social
network analysis
• It measures how important is a node with
respect to its nearest neighbors
Fundamental Ideas
• AB, AE, and BE have path length of 1 (1 line connects each
pair of points)
• A and C are connected through B and have a path length of 2
(2 lines)
• there are no isolated points
• every point can reach every other point within 2 steps
A
C
B
D
E
Fundamental Ideas
• AD has a path lenth of 1
• the walk ABCAD is not a path (passes through A twice!)
• ABCD has a path length of 3
• A and D are connected by 3 paths
AD – length 1
ACD – length 2
ABCD – length 3
- the distance between A and D is equal to the shortest path
A
B
D
C
Fundamental Ideas
• directed graphs are similar except for the possible assymetry of
the relationship
• degree has two separate components:
indegree: total numbers of alters related to ego; A=1, B=2, C=1
outdegree: total numbers of points ego relates to; A=1 , B=1 , C=2
paths: CAB is a path, CBA is not a path!
B
A
C
Graph Density
• describes the general level of contectedness in a graph
• graph is complete if all points are adjacent to each other
• the more points that are connected, the greater the density
• there are two components for density
inclusiveness: number of points that are included in the graph
because they are connected
total degree: sum of degree of all the points
Graph Density
Density is defined as the total number of observed lines in a
graph divided by the total number of possible lines in the
same graph
Density ranges from 0 to 1
L
D =
2L
=
g * (g-1)
2
L = number of lines;
g * (g-1)
g = number of points
Graph Density Examples