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Networks & Health
Intro & overview
Dropbox: https://tinyurl.com/SN-H2018
1. Intro/Big Picture
1. What are networks?
2. Connections & Positions
2. Network Relevance to Health Research
3. Basic Network Data Elements
1. Types of networks
2. Levels of analysis
3. Data structures
Outline
Social Network Data
Introduction
We live in a connected world:
“To speak of social life is to speak of the association between
people – their associating in work and in play, in love and in
war, to trade or to worship, to help or to hinder. It is in the
social relations men establish that their interests find
expression and their desires become realized.”
Peter M. Blau
Exchange and Power in Social Life, 1964
*1934, NYTime. Moreno claims this work was covered in “all the major papers” but I can’t find any other clips…
*
Introduction
We live in a connected world:
"If we ever get to the point of charting a whole city or a whole nation, we would have … a picture
of a vast solar system of intangible structures, powerfully influencing conduct, as gravitation does
in space. Such an invisible structure underlies society and has its influence in determining the
conduct of society as a whole."
J.L. Moreno, New York Times, April 13, 1933
But scientists are starting to take network seriously:
“Networks”
Introduction
“Networks”
“Obesity”
Introduction
But scientists are starting to take network seriously: why?
Introduction
…and NSF is investing heavily in it.
High Schools as Networks
Introduction
Introduction
Countryside High School, by grade
Introduction
Countryside High School, by race
And yet, standard social science analysis methods do not take this space
into account.
“For the last thirty years, empirical social research has been
dominated by the sample survey. But as usually practiced, …, the
survey is a sociological meat grinder, tearing the individual from his
social context and guaranteeing that nobody in the study interacts
with anyone else in it.”
Allen Barton, 1968 (Quoted in Freeman 2004)
Moreover, the complexity of the relational world makes it impossible to
identify social connectivity using only our intuition.
Social Network Analysis (SNA) provides a set of tools to empirically
extend our theoretical intuition of the patterns that compose social
structure.
Introduction
Social network analysis is:
•a set of relational methods for systematically understanding
and identifying connections among actors. SNA
•is motivated by a structural intuition based on ties
linking social actors
•is grounded in systematic empirical data
•draws heavily on graphic imagery
•relies on the use of mathematical and/or computational
models.
•Social Network Analysis embodies a range of theories
relating types of observable social spaces and their relation
to individual and group behavior.
Introduction
Social Determinants of Health
“…social determinants of health refers to the complex, integrated, and overlapping
social structures and economic systems that include social and physical environments
and health services.” (CDC, 2010)
WHO Commission on Social Determinants of Health Conceptual Framework
Introduction
Social Determinants of Health
Social factors matter
RWJ, Health Affairs (2014) “The relative contributions of multiple determinants to health outcomes”
Introduction
Social Determinants of Health
Social effects hold promising multiplier effects:
Introduction
History of SN&H
Social Science & Medicine, 2000
ASR
AJS
AJPH
Science
Social
Networks
PUBLIC HEALTH REPORTS, 1998
Mark S. Handcock, David R. Hunter,
Carter T. Butts, Steven M. Goodreau, and
Martina Morris (2003).
statnet: Software tools for the Statistical
Modeling of Network Data. URL
http://statnetproject.org
State of the field
Trends
English language Articles indexed in Web of Science Social
Science Citation Index on: ("health" or "well being" or
"medicine") and "network*").
There have been 18572 such papers since 2000.
State of the field
Big-Picture
Bibliographic Similarity Networks: 1-step neighborhood of a single paper
State of the field
Big-Picture
Bibliographic Similarity Networks: 2-step neighborhood of a single paper
State of the field
Big-Picture
Since the net is large…
Use a force-directed layout to display the full space & overlay clusters….
The example paper…
Modularity:
Top-Level: 0.798 @ 32 Clusters
2nd Level: 0.785 @ 150 Clusters
Rogers:
Valente: Various
Christakis & Fowler
Martina Morris: Concurrency
Heckathorn: RDS
House: Social Relations
& Health
Provan: Network
Effectiveness
Add Health
Ellison et al: Facebook
Edward Laumann
Pescosolido
Introduction
Network Research Lifecycle
Introduction
Key Questions
Social Network analysis lets us answer questions about social interdependence.
These include:
“Networks as Variables” approaches
•Are kids with smoking peers more likely to smoke themselves?
•Do unpopular kids get in more trouble than popular kids?
•Do central actors control resources?
“Networks as Structures” approaches
•What generates hierarchy in social relations?
•What network patterns spread diseases most quickly?
•How do role sets evolve out of consistent relational activity?
Both: Connectionist vs. Positional features of the network
We don’t want to draw this line too sharply: emergent role positions can
affect individual outcomes in a ‘variable’way, and variable approaches
constrain relational activity.
Why do networks matter?
Two fundamental mechanisms: Problem space
Connectionist:
Positional:
Networks as pipes
Networks as roles
Networks
As Cause
Networks
As Result
Diffusion
Peer influence
Social Capital
“small worlds”
Social integration
Peer selection
Homophily
Network robustness
Popularity Effects
Role Behavior
Network Constraint
Group stability
Network ecology
“Structuration”
This rubric is organized around social mechanisms – the reasons why networks matter,
which ends up being loosely correlated with specific types of measures, analysis, and
data collection method.
Why do networks matter?
Two fundamental mechanisms: Connections
Connectionist network mechanisms : Networks matter because of the
things that flow through them. Networks as pipes.
C
P
X Y
The spread of any epidemic depends on the number of
secondary cases per infected case, known as the
reproductive rate (R0). R0 depends on the probability that
a contact will be infected over the duration of contact (b),
the likelihood of contact (c), and the duration of
infectiousness (D).
cDRo b
For network transmission problems, the trick is specifying c,
which depends on the network.
C
P
X Y
Why do networks matter?
Two fundamental mechanisms: Connections example
Isolated visionWhy do networks matter?
Two fundamental mechanisms: Connections example
C
P
X Y
Connected visionWhy do networks matter?Why do networks matter?
Two fundamental mechanisms: Connections example
C
P
X Y
Partner
Distribution
Component
Size/Shape
Emergent Connectivity in “low-degree” networks
C
P
X Y
Connections: Diffusion
Example: Small local changes can create cohesion
cascades
Based on work supported by R21-HD072810 (NICHD, Moody PI), R01 DA012831-05 (NIDA Morris, Martina PI)
Provides food for
Romantic Love
Bickers with
Why do networks matter?
Two fundamental mechanisms: Positions
Positional network mechanisms : Networks matter because of the way they
capture role behavior and social exchange. Networks as Roles.
C
P
X Y
Parent Parent
Child
Child
Child
Provides food for
Romantic Love
Bickers with
Why do networks matter?
Two fundamental mechanisms: Positions
Positional network mechanisms : Networks matter because of the way they
capture role behavior and social exchange. Networks as Roles.
C
P
X Y
The unit of interest in a network are the combined sets of
actors and their relations.
We represent actors with points and relations with lines.
Actors are referred to variously as:
Nodes, vertices or points
Relations are referred to variously as:
Edges, Arcs, Lines, Ties
Example:
a
b
c e
d
Social Network Data
In general, a relation can be:
Binary or Valued
Directed or Undirected
a
b
c e
d
Undirected, binary Directed, binary
a
b
c e
d
a
b
c e
d
Undirected, Valued Directed, Valued
a
b
c e
d
1 3
4
21
Social Network Data
In general, a relation can be: (1) Binary or Valued (2) Directed or Undirected
Social Network Data
Basic Data Elements
The social process of interest will often determine what form your data take. Conceptually, almost
all of the techniques and measures we describe can be generalized across data format, but you may
have to do some of the coding work yourself….
a
b
c e
d
Directed,
Multiplex categorical edges
We can examine networks across multiple levels:
1) Ego-network
- Have data on a respondent (ego) and the people they are connected to
(alters). Example: 1985 GSS module
- May include estimates of connections among alters
2) Partial network
- Ego networks plus some amount of tracing to reach contacts of
contacts
- Something less than full account of connections among all pairs of
actors in the relevant population
- Example: CDC Contact tracing data for STDs
Social Network Data
Basic Data Elements: Levels of analysis
3) Complete or “Global” data
- Data on all actors within a particular (relevant) boundary
- Never exactly complete (due to missing data), but boundaries are set
-Example: Coauthorship data among all writers in the social
sciences, friendships among all students in a classroom
We can examine networks across multiple levels:
Social Network Data
Basic Data Elements: Levels of analysis
Ego-Net
Global-Net
Best Friend
Dyad
Primary
Group
Social Network Data
Basic Data Elements: Levels of analysis
2-step
Partial network
Social Network Data
Social network data are substantively divided by the number of
modes in the data.
1-mode data represents edges based on direct contact between
actors in the network. All the nodes are of the same type (people,
organization, ideas, etc). Examples:Communication, friendship,
giving orders, sending email.
This is commonly
what people think
about when
thinking about
networks: nodes
having direct
relations with
each other.
Social Network Data
Social network data are substantively divided by the number of
modes in the data.
2-mode data represents nodes from two separate classes, where
all ties are across classes. Examples:
People as members of groups
People as authors on papers
Words used often by people
Events in the life history of people
The two modes of the data represent a duality: you can project
the data as people connected to people through joint membership
in a group, or groups to each other through common membership
There may be multiple relations of multiple types connecting
your nodes.
Bipartite networks imply a constraint on the mixing, such that ties only cross classes.
Here we see a tie connecting each woman with the party she attended (Davis data)
Social Network Data
Basic Data Elements: Modes
Social Network Data
Basic Data Elements: Modes
Bipartite networks imply a constraint on the mixing, such that ties only cross classes.
Here we see a tie connecting each woman with the party she attended (Davis data)
By projecting the data, one can look at the shared between people or the common
memberships in groups: this is the person-to-person projection of the 2-mode data.
Social Network Data
Basic Data Elements: Modes
Social Network Data
Basic Data Elements: Modes
By projecting the data, one can look at the shared between people or the common
memberships in groups: this is the group-to-group projection of the 2-mode data.
Social Network Data
Example of a 2-mode
network: faculty
supervising students
- Any list of what
people do –
meetings, clubs,
activities, co-
authorship, – that
they do with others
forms network data.
Moody
The Movement of Carbapenem-Resistant Klebsiella pneumoniae among Healthcare Facilities: A Network Analysis
D van Duin, F Perez, E Cober, SS Richter, RC Kalayjian, RA Salata, N Scalera, R Watkins, Y Doi, S Evans, VG Fowler Jr, KS Kaye, SD Rudin, KM Hujer, AM Hujer,
RA Bonomo, and J Moody for the Antibacterial Resistance Leadership Group
Social Network Data
Example of a 2-mode network: Patients & Care Settings
Casalino, Lawrence P., Michael F. Pesko, Andrew M. Ryan, David J. Nyweide, Theodore J. Iwashyna, Xuming Sun, Jayme Mendelsohn and James
Moody. “Physician Networks and Ambulatory Care Admissions” Medical Care 53:534-41
Social Network Data
Example of a 2-mode network: Patients & Care Settings
From pictures to matrices
a
b
c e
d
Undirected, binary
a b c d e
a
b
c
d
e
1
1 1
1 1 1
1 1
1 1
An undirected graph and the
corresponding matrix is symmetric.
The traditional way to store & represent
network data is with an adjacency matrix.
The matrix (X) at right represents an
undirected binary network. Each node (a-e)
is listed on both the row and the column.
The ith row and the jth column (Xij) records the
value of a tie from node i to node j. For
example, the line between nodes a and b is
represented as an entry in the first row and
second column (red at right).
Because the graph is undirected the ties sent
are the same as the ties receive, so every entry
above the diagonal equals the entries below
the diagonal.
Basic Data Structures
Social Network Data
Directed, binary
a
b
c e
d
a b c d e
a
b
c
d
e
1
1
1 1 1
1 1
A directed graph and the
corresponding matrix is asymmetrical.
Directed graphs, on the other hand,
are asymmetrical.
We can see that Xab =1 and Xba =1,
therefore a “sends” to b and b “sends” to a.
However, Xbc=0 while Xcb=1; therefore,
c “sends” to b, but b does not reciprocate.
Basic Data Structures
Social Network Data
a b c d e
a
b
c
d
e
1
3
1 2 4
2 1
A directed graph and the
corresponding matrix is asymmetrical.
Directed graphs, on the other hand,
are asymmetrical.
We can see that Xab =1 and Xba =1,
therefore a “sends” to b and b “sends” to a.
However, Xbc=0 while Xcb=1; therefore,
c “sends” to b, but b does not reciprocate.
Basic Data Structures
Social Network Data
Directed, Valued
a
b
c e
d
From matrices to lists (binary)
a b c d e
a
b
c
d
e
1
1 1
1 1 1
1 1
1 1
a b
b a c
c b d e
d c e
e c d
a b
b a
b c
c b
c d
c e
d c
d e
e c
e d
Adjacency List
Arc List
Social network analysts also use adjacency lists and arc lists
to more efficiently store network data.
a
b
c e
d
Basic Data Structures
Social Network Data
From matrices to lists (valued)
a b c d e
a
b
c
d
e
1
1 2
2 3 5
3 1
5 1
a b
b a c
c b d e
d c e
e c d
a b 1
b a 1
b c 2
c b 2
c d 3
c e 5
d c 3
d e 1
e c 5
e d 1
Adjacency List
Arc List
Social network analysts also use adjacency lists and arc lists
to more efficiently store network data.
a
b
c e
d
Basic Data Structures
Social Network Data
1 2
5
13 a 1
b 1 2
c 2 3 1
d 3 1
e 5 1
contact value
Working with two-mode data
A person-to-group adjacency matrix is rectangular, with one mode
(persons, say) down rows and the other (groups, say) across columns
1 2 3 4 5
A 0 0 0 0 1
B 1 0 0 0 0
C 1 1 0 0 0
D 0 1 1 1 1
E 0 0 1 0 0
F 0 0 1 1 0
A =
Each column is a group,
each row a person, and
the cell = 1 if the person in
that row belongs to that
group.
You can tell how many
groups two people both
belong to by comparing
the rows: Identify every
place that both rows = 1,
sum them, and you have
the overlap.
Basic Data Structures
Social Network Data
Overview
SN&H Program
Overview
SN&H Program
Overview
SN&H Program
Overview
SN&H Program
Overview
SN&H Program
Overview
SN&H Program
Overview
SN&H Program
Overview
SN&H Program
Who are you?
SN&H Program
Thanks to DuPRI, DNAC Staff, SSRI, NICHD
SN&H Program

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00 Introduction to SN&H: Key Concepts and Overview

  • 1. Networks & Health Intro & overview Dropbox: https://tinyurl.com/SN-H2018
  • 2. 1. Intro/Big Picture 1. What are networks? 2. Connections & Positions 2. Network Relevance to Health Research 3. Basic Network Data Elements 1. Types of networks 2. Levels of analysis 3. Data structures Outline Social Network Data
  • 3. Introduction We live in a connected world: “To speak of social life is to speak of the association between people – their associating in work and in play, in love and in war, to trade or to worship, to help or to hinder. It is in the social relations men establish that their interests find expression and their desires become realized.” Peter M. Blau Exchange and Power in Social Life, 1964
  • 4. *1934, NYTime. Moreno claims this work was covered in “all the major papers” but I can’t find any other clips… * Introduction We live in a connected world: "If we ever get to the point of charting a whole city or a whole nation, we would have … a picture of a vast solar system of intangible structures, powerfully influencing conduct, as gravitation does in space. Such an invisible structure underlies society and has its influence in determining the conduct of society as a whole." J.L. Moreno, New York Times, April 13, 1933
  • 5. But scientists are starting to take network seriously: “Networks” Introduction
  • 6. “Networks” “Obesity” Introduction But scientists are starting to take network seriously: why?
  • 7. Introduction …and NSF is investing heavily in it.
  • 8. High Schools as Networks Introduction
  • 11. And yet, standard social science analysis methods do not take this space into account. “For the last thirty years, empirical social research has been dominated by the sample survey. But as usually practiced, …, the survey is a sociological meat grinder, tearing the individual from his social context and guaranteeing that nobody in the study interacts with anyone else in it.” Allen Barton, 1968 (Quoted in Freeman 2004) Moreover, the complexity of the relational world makes it impossible to identify social connectivity using only our intuition. Social Network Analysis (SNA) provides a set of tools to empirically extend our theoretical intuition of the patterns that compose social structure. Introduction
  • 12. Social network analysis is: •a set of relational methods for systematically understanding and identifying connections among actors. SNA •is motivated by a structural intuition based on ties linking social actors •is grounded in systematic empirical data •draws heavily on graphic imagery •relies on the use of mathematical and/or computational models. •Social Network Analysis embodies a range of theories relating types of observable social spaces and their relation to individual and group behavior. Introduction
  • 13. Social Determinants of Health “…social determinants of health refers to the complex, integrated, and overlapping social structures and economic systems that include social and physical environments and health services.” (CDC, 2010) WHO Commission on Social Determinants of Health Conceptual Framework Introduction
  • 14. Social Determinants of Health Social factors matter RWJ, Health Affairs (2014) “The relative contributions of multiple determinants to health outcomes” Introduction
  • 15. Social Determinants of Health Social effects hold promising multiplier effects: Introduction
  • 17.
  • 18.
  • 19.
  • 20. Social Science & Medicine, 2000
  • 21.
  • 22.
  • 23.
  • 25.
  • 26.
  • 27.
  • 28.
  • 30.
  • 32. Mark S. Handcock, David R. Hunter, Carter T. Butts, Steven M. Goodreau, and Martina Morris (2003). statnet: Software tools for the Statistical Modeling of Network Data. URL http://statnetproject.org
  • 33.
  • 34.
  • 35.
  • 36.
  • 37.
  • 38. State of the field Trends English language Articles indexed in Web of Science Social Science Citation Index on: ("health" or "well being" or "medicine") and "network*"). There have been 18572 such papers since 2000.
  • 39. State of the field Big-Picture Bibliographic Similarity Networks: 1-step neighborhood of a single paper
  • 40. State of the field Big-Picture Bibliographic Similarity Networks: 2-step neighborhood of a single paper
  • 41. State of the field Big-Picture Since the net is large… Use a force-directed layout to display the full space & overlay clusters….
  • 43. Modularity: Top-Level: 0.798 @ 32 Clusters 2nd Level: 0.785 @ 150 Clusters
  • 45.
  • 53. Ellison et al: Facebook
  • 56.
  • 57.
  • 58.
  • 60. Introduction Key Questions Social Network analysis lets us answer questions about social interdependence. These include: “Networks as Variables” approaches •Are kids with smoking peers more likely to smoke themselves? •Do unpopular kids get in more trouble than popular kids? •Do central actors control resources? “Networks as Structures” approaches •What generates hierarchy in social relations? •What network patterns spread diseases most quickly? •How do role sets evolve out of consistent relational activity? Both: Connectionist vs. Positional features of the network We don’t want to draw this line too sharply: emergent role positions can affect individual outcomes in a ‘variable’way, and variable approaches constrain relational activity.
  • 61. Why do networks matter? Two fundamental mechanisms: Problem space Connectionist: Positional: Networks as pipes Networks as roles Networks As Cause Networks As Result Diffusion Peer influence Social Capital “small worlds” Social integration Peer selection Homophily Network robustness Popularity Effects Role Behavior Network Constraint Group stability Network ecology “Structuration” This rubric is organized around social mechanisms – the reasons why networks matter, which ends up being loosely correlated with specific types of measures, analysis, and data collection method.
  • 62. Why do networks matter? Two fundamental mechanisms: Connections Connectionist network mechanisms : Networks matter because of the things that flow through them. Networks as pipes. C P X Y
  • 63. The spread of any epidemic depends on the number of secondary cases per infected case, known as the reproductive rate (R0). R0 depends on the probability that a contact will be infected over the duration of contact (b), the likelihood of contact (c), and the duration of infectiousness (D). cDRo b For network transmission problems, the trick is specifying c, which depends on the network. C P X Y Why do networks matter? Two fundamental mechanisms: Connections example
  • 64. Isolated visionWhy do networks matter? Two fundamental mechanisms: Connections example C P X Y
  • 65. Connected visionWhy do networks matter?Why do networks matter? Two fundamental mechanisms: Connections example C P X Y
  • 66. Partner Distribution Component Size/Shape Emergent Connectivity in “low-degree” networks C P X Y Connections: Diffusion Example: Small local changes can create cohesion cascades Based on work supported by R21-HD072810 (NICHD, Moody PI), R01 DA012831-05 (NIDA Morris, Martina PI)
  • 67. Provides food for Romantic Love Bickers with Why do networks matter? Two fundamental mechanisms: Positions Positional network mechanisms : Networks matter because of the way they capture role behavior and social exchange. Networks as Roles. C P X Y
  • 68. Parent Parent Child Child Child Provides food for Romantic Love Bickers with Why do networks matter? Two fundamental mechanisms: Positions Positional network mechanisms : Networks matter because of the way they capture role behavior and social exchange. Networks as Roles. C P X Y
  • 69. The unit of interest in a network are the combined sets of actors and their relations. We represent actors with points and relations with lines. Actors are referred to variously as: Nodes, vertices or points Relations are referred to variously as: Edges, Arcs, Lines, Ties Example: a b c e d Social Network Data
  • 70. In general, a relation can be: Binary or Valued Directed or Undirected a b c e d Undirected, binary Directed, binary a b c e d a b c e d Undirected, Valued Directed, Valued a b c e d 1 3 4 21 Social Network Data
  • 71. In general, a relation can be: (1) Binary or Valued (2) Directed or Undirected Social Network Data Basic Data Elements The social process of interest will often determine what form your data take. Conceptually, almost all of the techniques and measures we describe can be generalized across data format, but you may have to do some of the coding work yourself…. a b c e d Directed, Multiplex categorical edges
  • 72. We can examine networks across multiple levels: 1) Ego-network - Have data on a respondent (ego) and the people they are connected to (alters). Example: 1985 GSS module - May include estimates of connections among alters 2) Partial network - Ego networks plus some amount of tracing to reach contacts of contacts - Something less than full account of connections among all pairs of actors in the relevant population - Example: CDC Contact tracing data for STDs Social Network Data Basic Data Elements: Levels of analysis
  • 73. 3) Complete or “Global” data - Data on all actors within a particular (relevant) boundary - Never exactly complete (due to missing data), but boundaries are set -Example: Coauthorship data among all writers in the social sciences, friendships among all students in a classroom We can examine networks across multiple levels: Social Network Data Basic Data Elements: Levels of analysis
  • 74. Ego-Net Global-Net Best Friend Dyad Primary Group Social Network Data Basic Data Elements: Levels of analysis 2-step Partial network
  • 75. Social Network Data Social network data are substantively divided by the number of modes in the data. 1-mode data represents edges based on direct contact between actors in the network. All the nodes are of the same type (people, organization, ideas, etc). Examples:Communication, friendship, giving orders, sending email. This is commonly what people think about when thinking about networks: nodes having direct relations with each other.
  • 76. Social Network Data Social network data are substantively divided by the number of modes in the data. 2-mode data represents nodes from two separate classes, where all ties are across classes. Examples: People as members of groups People as authors on papers Words used often by people Events in the life history of people The two modes of the data represent a duality: you can project the data as people connected to people through joint membership in a group, or groups to each other through common membership There may be multiple relations of multiple types connecting your nodes.
  • 77. Bipartite networks imply a constraint on the mixing, such that ties only cross classes. Here we see a tie connecting each woman with the party she attended (Davis data) Social Network Data Basic Data Elements: Modes
  • 78. Social Network Data Basic Data Elements: Modes Bipartite networks imply a constraint on the mixing, such that ties only cross classes. Here we see a tie connecting each woman with the party she attended (Davis data)
  • 79. By projecting the data, one can look at the shared between people or the common memberships in groups: this is the person-to-person projection of the 2-mode data. Social Network Data Basic Data Elements: Modes
  • 80. Social Network Data Basic Data Elements: Modes By projecting the data, one can look at the shared between people or the common memberships in groups: this is the group-to-group projection of the 2-mode data.
  • 81. Social Network Data Example of a 2-mode network: faculty supervising students - Any list of what people do – meetings, clubs, activities, co- authorship, – that they do with others forms network data. Moody
  • 82. The Movement of Carbapenem-Resistant Klebsiella pneumoniae among Healthcare Facilities: A Network Analysis D van Duin, F Perez, E Cober, SS Richter, RC Kalayjian, RA Salata, N Scalera, R Watkins, Y Doi, S Evans, VG Fowler Jr, KS Kaye, SD Rudin, KM Hujer, AM Hujer, RA Bonomo, and J Moody for the Antibacterial Resistance Leadership Group Social Network Data Example of a 2-mode network: Patients & Care Settings
  • 83. Casalino, Lawrence P., Michael F. Pesko, Andrew M. Ryan, David J. Nyweide, Theodore J. Iwashyna, Xuming Sun, Jayme Mendelsohn and James Moody. “Physician Networks and Ambulatory Care Admissions” Medical Care 53:534-41 Social Network Data Example of a 2-mode network: Patients & Care Settings
  • 84. From pictures to matrices a b c e d Undirected, binary a b c d e a b c d e 1 1 1 1 1 1 1 1 1 1 An undirected graph and the corresponding matrix is symmetric. The traditional way to store & represent network data is with an adjacency matrix. The matrix (X) at right represents an undirected binary network. Each node (a-e) is listed on both the row and the column. The ith row and the jth column (Xij) records the value of a tie from node i to node j. For example, the line between nodes a and b is represented as an entry in the first row and second column (red at right). Because the graph is undirected the ties sent are the same as the ties receive, so every entry above the diagonal equals the entries below the diagonal. Basic Data Structures Social Network Data
  • 85. Directed, binary a b c e d a b c d e a b c d e 1 1 1 1 1 1 1 A directed graph and the corresponding matrix is asymmetrical. Directed graphs, on the other hand, are asymmetrical. We can see that Xab =1 and Xba =1, therefore a “sends” to b and b “sends” to a. However, Xbc=0 while Xcb=1; therefore, c “sends” to b, but b does not reciprocate. Basic Data Structures Social Network Data
  • 86. a b c d e a b c d e 1 3 1 2 4 2 1 A directed graph and the corresponding matrix is asymmetrical. Directed graphs, on the other hand, are asymmetrical. We can see that Xab =1 and Xba =1, therefore a “sends” to b and b “sends” to a. However, Xbc=0 while Xcb=1; therefore, c “sends” to b, but b does not reciprocate. Basic Data Structures Social Network Data Directed, Valued a b c e d
  • 87. From matrices to lists (binary) a b c d e a b c d e 1 1 1 1 1 1 1 1 1 1 a b b a c c b d e d c e e c d a b b a b c c b c d c e d c d e e c e d Adjacency List Arc List Social network analysts also use adjacency lists and arc lists to more efficiently store network data. a b c e d Basic Data Structures Social Network Data
  • 88. From matrices to lists (valued) a b c d e a b c d e 1 1 2 2 3 5 3 1 5 1 a b b a c c b d e d c e e c d a b 1 b a 1 b c 2 c b 2 c d 3 c e 5 d c 3 d e 1 e c 5 e d 1 Adjacency List Arc List Social network analysts also use adjacency lists and arc lists to more efficiently store network data. a b c e d Basic Data Structures Social Network Data 1 2 5 13 a 1 b 1 2 c 2 3 1 d 3 1 e 5 1 contact value
  • 89. Working with two-mode data A person-to-group adjacency matrix is rectangular, with one mode (persons, say) down rows and the other (groups, say) across columns 1 2 3 4 5 A 0 0 0 0 1 B 1 0 0 0 0 C 1 1 0 0 0 D 0 1 1 1 1 E 0 0 1 0 0 F 0 0 1 1 0 A = Each column is a group, each row a person, and the cell = 1 if the person in that row belongs to that group. You can tell how many groups two people both belong to by comparing the rows: Identify every place that both rows = 1, sum them, and you have the overlap. Basic Data Structures Social Network Data
  • 98. Who are you? SN&H Program
  • 99. Thanks to DuPRI, DNAC Staff, SSRI, NICHD SN&H Program