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Social Network Analysis
Steve Borgatti
Carroll School of Management, Boston College
© Steve Borgatti, 2004
Development of the Field
600
500
•
•
1736 – Euler
1930s Sociometry
•
1940s Psychologists
•
1950s Anthropologists
•
1960s Anthropologists
•
1970s Rise of Sociologists
•
1980s Computation
•
1990s Adaptive Radiation
400
300
200
100
0
1960
0.134x
y = 0.001e
2
R = 0.917
1970
1980
1990
# of SNA papers in
sociology by year
2000
2010
•
–
Moreno; Hawthorne studies
–
Clique formally defined
–
Barnes, Bott & Manchester school
–
Kinship algebras; Mitchell
–
–
–
Social Networks Journal & Assoc
Milgram small-world
Granovetter’s weak ties
–
IBM PC & network programs
–
–
UCINET IV released
Spread of networks & dyadic
thinking to many fields
Rise of social capital, embeddedness
–
2000s Locusts Physicists descend
© Steve Borgatti, 2004
What’s a network?
• A set of actors (e.g., persons)
• A set of ties that connect pairs of
actors
– E.g., friendship ties
• Each kind of tie (i.e., social relation)
defines a different network
–
–
–
–
–
–
Acquaintance (who knows whom)
Friendship
Has sex with
Does drugs with
Gives advice to
Has conflict with
1000 scientists
© Steve Borgatti, 2004
Why should we care?
1. It’s not just the elements (composition) of a system
that matter, but how they are put together
–
non-reductionist, holistic, structuralist
© Steve Borgatti, 2004
2. Actors affect each other!
PA
1
LA
5
GA
2
GA
1
•
•
•
•
FL
2
Tell each other information
Provide material aid
Transmit diseases
Copy attitudes & behavior
LA
4
TX
1
FL
1
LA
1
LA
2
LA
3
NY
10
NY
12
NY
2
LA
8
LA
9
NY
3
LA
7
NY
5
LA
6
NY
13
NY
19
SF
1
NY
11
NY
21
NY
4
0
NY
9
NY
15
NY
8
NY
14
NJ
1
NY
16
U.S. Centers for Disease Control
NY
1
NY
17
NY
18
NY
22
NY7
NY
20
NY
6
© Steve Borgatti, 2004
3. Opportunities & constraints
• A person’s position in a social network (i.e., social
capital) determines in part the set of opportunities
and constraints they will encounter
Maire Messenger Davies
© Steve Borgatti, 2004
The rate of return on human capital
• A person’s connections determine the rate of return
on human capital
Human
capital
profit
rate of
return
social capital
© Steve Borgatti, 2004
Kinds of Nodes
• Individuals
– persons
– other animals
• Collectivities
– organizations, departments, teams, troops
– countries, cities
– species
© Steve Borgatti, 2004
Social Relations Among Persons
• Kinship
– mother of
• Other social role-based
– boss of, friend of
• Cognitive/perceptual
– knows
– aware of what they know
• Affective
– likes
– trusts
• Interactions
– give advice, talks to
– sex / drugs with
• Affiliations
– belong to same clubs
– is physically near
© Steve Borgatti, 2004
Simple Answers
Who you ask for answers to straightforward questions.
HR Dept
of Large
Health Care
Organization
Recent acquisition
Older acquisitions
Original company
Data drawn from Cross, Borgatti & Parker 2001.
© Steve Borgatti, 2004
Problem Reformulation
Who you see to help you think through issues
Recent acquisition
Older acquisitions
Original company
Data drawn from Cross, Borgatti & Parker 2001.
© Steve Borgatti, 2004
Hawthorne Games & Conflicts
I3
S2
I3
S2
S4
S4
S1
S1
W4
W2
W9
W2
W5
W7
W9
W1
W1
W5
W7
W8
W8
I1
I1
W4
W3
W3
W6
W6
© Steve Borgatti, 2004
Combining Games & Fights
I3
S2
S4
S1
W4
W9
W2
W5
W7
W1
I1
W8
W3
GREEN = games only
RED = fights only
BLACK = games & fights
W6
© Steve Borgatti, 2004
Relations Among Orgs
• As corporate entities
– sells to, leases to, lends to, outsources to
– joint ventures, alliances, invests in, subsidiary
– regulates
• Through members
– ex-member of (personnel flow)
– interlocking directorates
– all social relations
© Steve Borgatti, 2004
Internet Alliances
Microsoft
AOL
Yahoo
AT&T
© Steve Borgatti, 2004
Co-Membership > 27%
PN
OCIS
HCM
CM
OM
GDO
ODC
MC
TIM
MH
HR
CAR
OB
OMT
BPS
IM
MSR
MOC
MED
SIM
ONE
RM
ENT
© Steve Borgatti, 2004
Network
Structure
© Steve Borgatti, 2004
The density of ties
• Density = proportion of pairs of actors that are actually tied
• In some contexts, could be thought of as measure of social capital
Low Density (25%)
High Density (39%)
© Steve Borgatti, 2004
Help With the Rice Harvest
Village 1
Data from
Entwistle et al
© Steve Borgatti, 2004
Help with the rice harvest
Which
village
is more
likely to
survive
?
Village 2
Data from
Entwistle et al
© Steve Borgatti, 2004
Small World
• Milgram’s experiment
– Target selected – a stock broker in Boston
– Arbitrary subjects recruited in Los Angeles
– Asked if they knew the target
• If yes, then done
• If no, then who did they know that might know the stock
broker?
– That person is then contacted and …
– This continues until the target is reached.
– On average, just 5.5 intermediaries needed to reach target
© Steve Borgatti, 2004
Austin Powers:
The spy who
shagged me
Let’s make
it legal
Robert Wagner
Wild Things
What Price Glory
Barry Norton
A Few
Good Men
Monsieur
Verdoux
© Steve Borgatti, 2004
Graph-Theoretic Distance
AKA “degrees of separation”
10
12
• The graph-theoretic distance
between two nodes is the number
of links in the shortest path that
connects them
11
8
9
– Distance from 4 to 10 is 3 links
2
3
7
1
4
6
5
© Steve Borgatti, 2004
Average Distance
• Average geodesic distance among all nodes
• Index of speed of transmission
Core/Periphery
c/p fit = 0.97, avg. dist. = 1.9
Clique structure
c/p fit = 0.33, avg. dist. = 2.4
© Steve Borgatti, 2004
Core/Periphery Structures
•
Core/Periphery.
– Network consists of a single group (a
core) together with hangers-on (a
periphery),
C/P struct.
• Core connects to all
• Periphery connects only to the core
– Short distances, good for transmitting
information, practices
– Identification with group as whole
– E.g., physics
•
Clique structure.
–
–
–
–
Multiple subgroups or factions
Identity with subgroup
Diversity of norms, belief
E.g., social science
Clique
struct.
© Steve Borgatti, 2004
On Innovation and Network Structure
“I would never have conceived my theory, let alone have
made a great effort to verify it, if I had been more
familiar with major developments in physics that were
taking place. Moreover, my initial ignorance of the
powerful, false objections that were raised against my
ideas protected those ideas from being nipped in the bud.”
– Michael Polanyi (1963), on a major contribution to physics
© Steve Borgatti, 2004
C/P Structures & Morale
50
„
45
Study by Jeff Johnson of a South
Pole scientific team over 8 months
40
„
35
Core/Periphery-ness
C/P structure seems to affect
morale
30
25
Group Morale
20
15
10
1
2
3
4
5
6
7
8
Month
Note: this is an© Steve
“n” Borgatti,
of 1 2004
Comparing airlines’ route structures
Major US Carrier
Note:
Source:
“Discount” US Airline
Route maps defined around one specific hub only
Industry data, BCG analysis
© Steve Borgatti, 2004
Eurocopa 2004
_PETIT
_PET IT
_QUIM
_QUIM
_MIGUEL
_MIGUEL
_NUNO_GOMES
_NUNO_GOMES
_BETO
_PAULETA
_BET O
_RICARDO_CARVALHO
_RICARDO_CARVALHO
_TIAGO
_PAULO_FERREIRA
_TIAGO
_PAULO_FERREIRA
_MOREIRA
_MOREIRA
Hélder_POSTIGA
Hélder_POSTIGA
_PAULETA
_NUNO_VALENTE
_NUNO_VALENTE
_DECO
_DECO
_RUI_COSTA
_MANICHE
_RUI_COST A
_COSTINHA
_MANICHE
_COSTINHA
_LUÍS_FIGO
_LUÍS_FIGO
_Sabrosa
Fernando_COUTO
Cristiano_RONALDO
_JORGE_ANDRADE
_Sabrosa
Fernando_COUTO
Cristiano_RONALDO
_JORGE_ANDRADE
_RUI_JORGE
_RUI_JORGE
_RICARDO
_RICARDO
Stylianos_VENETIDIS
Stylianos_VENETIDIS
Nikolaos_DABIZAS
Konstantinos_KATSOURANIS
Nikolaos_DABIZAS
Vassilios_TSIARTAS
Vassilios_TSIARTAS
Konstantinos_KATSOURANIS
T hemistoklis_NIKOLAIDIS
T hemistoklis_NIKOLAIDIS
Konstantinos_CHALKIAS
Konstantinos_CHALKIAS
T heofanis_KAT ERGIANNAKIS
T heofanis_KATERGIANNAKIS
Pantelis_KAFES
Angelos_CHARIST EAS
Giourkas_SEITARIDIS
Georgios_GEORGIADIS
Ioannis_GOUMAS
Pantelis_KAFES
Georgios_GEORGIADIS
Angelos_CHARISTEAS
Giourkas_SEITARIDIS
Ioannis_GOUMAS
Dimitrios_PAPADOPOULOS
Dimitrios_PAPADOPOULOS
Zisis_VRYZAS
Panagiotis_FYSSAS
Vassilios_LAKIS
Theodoros_ZAGORAKIS
Zisis_VRYZAS
Antonios_NIK
Traianos_DELLAS
Stylianos_GIANNAKOPOULOS
Angelos_BASINAS
Vassilios_LAKIS
Theodoros_ZAGORAKIS
Panagiotis_FYSSAS
Antonios_NIKOPOLIDIS
Traianos_DELLAS
Stylianos_GIANNAKOPOULOS
Mihalis_KAPSIS
Angelos_BASINAS
Mihalis_KAPSIS
Georgios_KARAGOUNIS
Georgios_KARAGOUNIS
© Steve Borgatti, 2004
Position in Networks
© Steve Borgatti, 2004
Carter Administration
White House Diary Data
Year 1
Year 4
Data ©
courtesy
of Michael
Link
Steve Borgatti,
2004
1-Mode Complete Network
Cultural interventions,
relationship building
Information
flow within
virtual group
New leader
Data warehousing,
systems architecture
© Steve
Borgatti, 2004
Cross, Parker, & Borgatti, 2002. Making Invisible Work Visible. California Management Review. 44(2):
25-46
Changes Made
• Cross-staffed new internal projects
– white papers, database development
• Established cross-selling sales goals
– managers accountable for selling projects with both kinds of
expertise
• New communication vehicles
– project tracking db; weekly email update
• Personnel changes
© Steve Borgatti, 2004
9 Months Later
Cross, Parker, & Borgatti, 2002. Making Invisible Work Visible. California Management Review. 44(2): 25-46
© Steve Borgatti, 2004
© Steve Borgatti, 2004