SOC 206

1
SOC 206

• INTRODUCTION TO
• NETWORK ANALYSIS I

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U.S. interstate highway system
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The switch yard at New York's Niagara Project
became useless metalwork when a blackout struck
the eastern United States
http//www.sfgate.com/cgi-bin/object/article?f/c/
a/2003/08/15/MN191082.DTLo0
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Network of physical interactions between nuclear
proteins ... consisting of all proteins that
are known to be localized in the yeast nucleus
..., and which interact with at least one other
protein in the nucleus. This subset consists of
318 interactions between 329 proteins. Note that
most neighbors of highly connected nodes have
rather low connectivity. Maslov and Sneppen
2002 http//arxiv.org/abs/cond-mat/0205380
Protein networks in yeast
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Spread of TB
Scientific collaboration
Black nodes are persons with clinical disease
(and are potentially infectious), pink nodes
represent exposed persons with incubating (or
dormant) infection and are not infectious, green
represent exposed persons with no infection and
are not infectious. The infection status is
unknown for the grey nodes. Unfortunately the
'social butterfly' in this community, the black
node in the center of the graph, is also the most
infectious -- a super spreader. http//www.orgnet.
com/contagion.html
The largest component of the Santa Fe Institute
collaboration network, with the primary divisions
detected by our algorithm indicated by different
vertex shapes. http//www.pnas.org/content/99/12/7
821.full.pdfhtml
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The Internet
http//www.lumeta.com/research/
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http//iserp.columbia.edu/files/iserp/2002_04.pdf
also as Berman et al. Chains of Affection, AJS
2004
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Management hierarchy of a major corporation and
decision-making conversations

• What do the decision-making links reveal about
  this organization?
• Some advice flows along formal ties within the
  hierarchy, while other advice flows along
  informal ties outside of the hierarchy.
• There is strong triangle of input and feedback
  amongst Directors 2 and 3 and the General
  Manager. These strong, trusting ties have grown
  and solidified over many years of working
  together.
• Director 1 is new to the organization. Manager
  12 was hoping to get this position, but Corporate
  strongly pushed for Director 1. Notice that
  Manager 12 is still locally influential in the
  decision-making network. Director 1 does not
  include input from direct reports in
  decision-making remember A --gt B means that A
  seeks out B !
• Director 4 is about to retire. He used to run
  this division when it was much smaller. Unlike
  Director 1, Director 4 does include inputs from
  his staff.
• The decision-making patterns in the departments
  of Directors 2 and 3 are quite different from the
  pattern of links in the departments of Directors
  1 and 4. Directors 2 and 3 seek information from
  all levels of the organization -- their
  departments show both vertical and horizontal
  flows. Several managers in these departments 23,
  24, 34, and 35 are boundary spanners --
  connecting to others outside of their immediate
  group. Departments 2 and 3 are an example of
  participatory decision-making -- including inputs
  from up and down the hierarchy, as well as inside
  and outside the department.
• Who do you see as the most influential
  persons in shaping decisions in this
  organization?

http//www.orgnet.com/decisions.html
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Interlocking Directorates in the Corporate
Community
http//sociology.ucsc.edu/whorulesamerica/power/co
rporate_community.html
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Political books purchased in August 2008 at
Amazon.com
Based on the pattern of connections between the
books in the map above, the most influential
political books at the end of the summer 2008
are What Happened (White House spokesman Scott
McClellans tell-all) and The Post American World
(Fareed Zakarias book on the rise of regional
powers -- neither addressed the ongoing election.
http//www.orgnet.com/divided.html
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Mark Lombardi Global (Conspiracy) Networks
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Social Network Analysis of the 9-11 Terrorist
Network
http//www.orgnet.com/hijackers.html
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http//socialsim.wordpress.com/2007/03/01/another-
fabulous-network-image-academy-award-thanks/
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World Trade in 1981 and 1992
Lothar Krempel. The structure of world trade of
between 28 OECD countries in 1981 and 1992. The
size of the nodes gives the volume of flows  in
dollars (imports and exports) for each country .
The size of the links stands for the volume of
trade between any two countries. Colors give
respectively the regional memberships in
different trade organisations EC countries
(yellow), EFTA countries (green), USA and Canada
(blue), Japan (red), East Asian Countries (pink),
Oceania (Australia , New Zealand) (black).
http//www.mpi-fg-koeln.mpg.de/lk/netvis/trade/W
orldTrade.html
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Social Network Analysis

• A network is a set of objects/nodes and a set of
  connections/ties between them
• In a social network, nodes can be people, groups,
  organizations, countries, physical or cultural
  objects created or used by people, peoples
  thoughts or activities, etc. just about anything
• Explanations based on network ties are usually
  categorized as network approach or structural
  approach
• SNA is mathematical, but not necessarily
  statistical
• SNA is not just about methods, its theory too

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Barbasi Scale-Free Networks

• Scale free networks obey the power law
• The power law posits that the distribution of
  links in a network follows a highly skewed
  distribution where a few has a great number of
  ties while the rest have few
• In a scale free network new nodes form
• by preferential attachment
• i.e. those with more connections will get even
  more
• This is also known as the Matthew principle
  (Merton)
• (see also rich gets richer, cumulative
  advantage,
• increasing returns to scale, network
  externalities)
• On the internet, the number of hyperlinks follow
  the power law.
• The more a site is linked the more new links it
  will attract. Hence you have a few giga sites
  like Google and millions of sites with only a few
  links to it.
• Some other examples
• Protein-to-protein interaction networks
• Sexual partners in humans
• Scientific citation networks
• Semantic networks

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Small World Studies

• Milgram (1967) gave a letter to people in
  Nebraska and Kansas to get it to a person in
  Massachusetts they did not know through personal
  acquaintances. The average number of steps was 5
  the maximum 12 and 25 of the letters arrived.
• Suppose each person knows 100 people (including
  the superficial acquaintances). Each person has
  100 degrees.
• Suppose there is no clustering. This person will
  have access to 100100 10 000 people in the
  second step. 100100100 1 million in the third.
  1004 100 million in the fourth and 10 billion in
  the fifth.

• Example of no clustering if everyone has only 4
  friends (the average degree is 4 with a variance
  of 0)

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• http//smallworld.columbia.edu/

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Six Degrees of Kevin Baconor Who is the Center
of the Hollywood Universe?

• 800,000 people in the Internet Movie Database
• Kevin Bacons number (average chain length) is
  2.946
• Sean Connerys number is 2
• Charlie Chaplins number is 3
• Jean-Luc Godards 2
• My father-in-law (Janos Hersko) has number 3
• Average for all 800,000 people is 9.200
• http//oracleofbacon.org/center.html

Bacon Number of people
0 1
1 1806
2 145024
3 395126
4 95497
5 7451
6 933
7 106
8 13
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Vertex nodes/objects, edgeties Newman 2003
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Forbidden Triad
Transitivity
C
C
A
B
A
B
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Granovetter The Strength of Weak Ties
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Burt Structural Holes

• The BEFORE network contains 5 primary contacts
  and reaches a total of 15 people. However, there
  are only two nonredundant contacts in the
  network. Contacts 2 and 3 are redundant in the
  sense of being connected with each other and
  reaching the same people. The same is true for
  contacts 4 and 5. Contact 1 is not connected
  directly to contact 2, but he reaches the same
  secondary contacts thus contacts 1 and 2 provide
  redundant network benefits. Illustrating the
  other extreme, contacts 3 and 5 are connected
  directly, but they are nonredundant because they
  reach separate clusters of secondary contacts.
• In the AFTER network, contact 2 is used to reach
  the first cluster in the BEFORE network, contact
  4 is used to reach the second cluster. The time
  and energy saved by withdrawing from relations
  with the other three primary contacts is
  reallocated to primary contacts in new clusters.
  The BEFORE and AFTER networks are both maintained
  at a cost of fice primary relationships, but the
  AFTER network is dramatically richer in
  structural holes, and so benefits." (Burt,
  Structural Holes pp.22-3.

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Robust Action and the Rise of the Medici

• Padgett and Ansell argue that the Medicis were
  powerful because they could use their membership
  in overlapping social networks strategically.
• Power comes from not being locked into a single
  network or identity but to cultivate ambiguity by
  belonging to many networks. Multiple networks
  also deliver more resources. Both ambiguity and
  multiple resources lead to more discretion and
  power.
• They could also attain central position where
  others had to communicate through them.

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Putnam Bowling Alone

• Social capital is declining
• Political participation is declining
• Participation in religious groups is declining
• Labor union membership is declining
• Participation in voluntary organizations is
  declining
• Family ties are looser
• Less contact with neighbors

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Wellman Cyberplace

• Larger volume and higher speed of information
  transfer
• Portability of wireless technology
• Globalized connectivity
• Personalization
• Networked individualism

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Cognitive Maps (Carley and Palmquist 1992)
This figure is a graphic illustration of the map
extracted from an interview with the same student
later in the term. This interview shows the
student's conception of research writing at the
end of the term. A comparison of Figure 4 and
Figure 5 shows that the student's conception has
shifted over time. For example, many of the
concepts used by the student to describe research
writing have changed and, for those concepts that
are retained, their relative semantic importance
may have changed (more important, more
relationships, more lines). From the beginning to
the end of the term, in the students mental model
of research writing, the concept information has
grown in importance (more lines in Figure 5 than
Figure 4) but the concept outline has decreased
in importance to the extent that it does not even
appear in the later map. Once again tracing
through some of the relationships between
concepts reveals that in the student's view, at
the end of the term, writing a paper involves
having information that depends on facts and a
plan that is original and guides research.
The figure is a graphic illustration of the
complete map extracted from the complete
interview with a student at the beginning of the
term . All concepts in the map are listed in a
circle. The relationship between two concepts is
denoted by a line. This map represents the
student's conception of research writing at the
beginning of the term, and it illustrates that
those concepts about which the student has the
most information at the beginning are fact,
research, topic, and writing. Tracing through
some of the relationships (represented by lines)
between concepts reveals that in the student's
view, at the beginning of the term, writing a
paper involves having an opinion that is based on
fact which can be found through research.
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Network Data

• Types of Questions asked
• Structural variables questions about
  ties/connections
• Compositional variables questions about
  characteristics/attributes of the nodes/actors
• When analyzing networks researchers often do not
  have representative samples of individuals
• Often creates human subject concerns
• Specifying boundaries of the population to study
• Nominalist approach actors themselves decide on
  membership in a network answering name generating
  questions
• Realist approach a list is constructed by a
  researcher based on theoretical concerns

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Snowball Sampling
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Types of Network Data One-Mode Network

• Actor-to-actor network
• Actor attributes characteristics of an actor
• Actors people, groups, organizations,
  communities, nations
• Relations interactions, transfer of resources or
  information, movement, formal roles, kinship
• E.g. Network data representing friendships among
  students in a high school
• This is a simple one-mode network data, where
  the relationships are binary (yes/no) and
  asymmetric, and we know one attribute about
  everyone (race)

Student 1 (W) Student 2 (H) Student 3 (B) . Student N (W)
Student 1 (W) X 1 1 . 1
Student 2 (H) 1 X 0 . 0
Student 3 (B) 1 0 X . 1
. . . . . .
Student N (W) 1 0 1 . X
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High school friendship (color is for race)
http//www.soc.washington.edu/users/stovel/Chains.
pdf
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Types of Network Data Dyadic Two-Mode
(Bipartite) Network
Lab2
Lab1

• Two sets of actors with connections only between
  the sets

Corporations
Nonprofits
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High school dating
Boy 1 Boy 2 Boy 3 . Boy M
Girl 1 0 1 1 . 1
Girl 2 0 0 0 . 0
Girl 3 1 0 0 . 1
. . . . . .
Girl N 0 0 1 . 0
http//www.soc.washington.edu/users/stovel/Chains.
pdf
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Types of Network Data Two-Mode, Affiliation
Network

• Actor-to-event network
• Actors are the first mode, events are the second
  mode
• Events are activities or groups that actors may
  participate in or be affiliated with
• Events social functions, clubs, voluntary
  organizations, agreements and treaties for
  countries, etc.
• Attributes are recorded for both actors and events

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Breiger Duality of Persons and Groups
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McPherson Hypernetwork Sampling
Sample of Individuals
Sample of Organizations
Org 1 Org 2 Org 3 Org 4 Org 5 Org 6 Org 7
Person 1 0 0 0 0 0 0 0
Person 2 0 0 0 0 0 0 0
Person 3 0 0 0 0 0 0 0
Person 4 0 0 0 0 0 0 0
Person 5 0 0 0 1 0 0 0
Person 6 0 1 0 0 0 0 1
Person 7 0 0 0 0 0 0 0
Person 8 0 0 0 0 1 0 0
Person 9 0 0 0 0 0 0 0
Person 10 0 0 0 0 0 0 0
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Types of Network Data Ego-Centered Network (GSS
1985)

• Also called personal network
• Centered on respondent
• Often used in surveys with representative samples
• Ego the focal actor
• Alter actors tied to an ego
• Attributes are recorded for both ego and alters
• Information on alters contacts with each other
  can be collected
• In most surveys, Egos connections to alters is
  ignored

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Quantifying Relationships

• Direction
• directed vs. symmetric (reciprocal) ties
• Level of measurement
• dichotomous vs. valued data
• Sign
• positive vs. negative

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Question Formats Roster vs. Free Recall

• Q1. This is a list of students taking Sociology
  101 with you. Please circle your own name. Please
  also indicate with an X with whom of these people
  you interact outside of class.
• Q2. Please think of up to three people you
  usually go to for an advice about your life and
  answer a few questions about them.

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Question Formats Free vs. Fixed Choice

• Q1. Please think of the people you usually go to
  for an advice about your life. Please write down
  their initials and answer a few questions about
  them.
• Q2. Please think of up to three people you
  usually go to for advice about your life and
  answer a few questions about them.

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Question Formats Ratings vs. Complete Rankings

• Q1. On a scale from 1 to 5 where 1 is not
  important at all and 5 is very important,
  please tell us how important this person is to
  you
• Q2. Please rank these persons in the order of
  importance to you with person number one being
  the most important.

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Summarizing Network Data

• Actor
• Dyad
• Triad
• Subgroup
• Set of actors
• Entire network

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Questionnaire

• Questions about graduate students and relations
  related to the studies
• How frequently do you talk to each person on this
  list (in person or on the phone)?
• With whom do you hang out discussing or debating
  sociological ideas?
• Who do you go to when you need help with your
  class work, paper, presentation or research?
• Who do you go to for advice or information on
  matters related to your studies (for example, who
  to choose as your advisor, which classes to take,
  which conference to attend, etc.)
• Who have you collaborated with on a class
  project, paper, conference presentation, or
  writing an article?
• Who do you go to when you face a stressful
  situation related to your graduate studies and
  want to talk to someone about it?
• If you receive good news related to your studies
  or professional career, who do you tell it to
  first?
• Questions about graduate students and relations
  beyond graduate studies
• Who do you go to for help when you need a 10
  loan, a ride to a doctor, etc.?
• Who do you go to when you face a stressful
  situation not related to your graduate studies
  and want to talk to someone about it?
• Who do you go to for advice or information when
  making life decisions not related to your
  studies?
• Who do you usually hang out with outside of the
  department socially (for example, visit each
  other for dinner or go to concerts, clubs, or
  parties together, etc.)?

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Questionnaire

• Questions about discussion/reading groups and
  classes
• Which of the following discussion/reading groups
  are you a regular participant of?
• Which of the following classes have you taken
  this academic year?
• Questions about faculty
• Which faculty members have you been in contact
  with beyond your class work this academic year
  (your worked for them as TA or RA, you joined
  their project, they are on your dissertation
  committee, etc.)

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Questionnaire

• Personal network questions
• Please write down initials of up to three people
  who you consider to be the most important people
  in your life and answer a few questions about
  them
• What is this persons gender?
• What is this persons age?
• How is this person related to you? (Please check
  all that apply)
• Does this person live in San Diego?
• How frequently do you see these people in person?
• How often to you talk to this person on the
  phone?
• How frequently to you email or text-message this
  person?
• Do you go to this person for help when you need a
  loan, a ride to a doctor, etc.?
• Do you go to this person when you face a
  stressful situation and want to talk to someone
  about it?
• Do you go to this person for advice or
  information when making life decisions?
• Do you spend your leisure time with this person
  (for example, visit each other for dinner or go
  to concerts, clubs, and parties together, etc.)?
• Who of the named people know each other, meet and
  talk to each other even when you are not around?

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Questionnaire

• Questions about the program
• Questions about satisfaction with the graduate
  school experience
• Demographic questions

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Academic Advice Network
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Student by Faculty Network
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Student by Courses Network