Difference between revisions of "MCSN Tuesday, 1-Nov-11"

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(Quiz #2 take 2)
(Applications: creating and manipulating two mode networks)
 
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= 4.8 =  
 
= 4.8 =  
 
* How to define the flying teams?
 
* How to define the flying teams?
= Affiliation networks =
+
= Chapter 5: Affiliation networks =
== Ideas ==
+
== Concepts ==
 +
=== Basic ideas ===
 
* People affiliate to groups (often defined by space, like the University of Alberta), and events (typically defined by space-time, like this class session), whether by choice or circumstance.  
 
* People affiliate to groups (often defined by space, like the University of Alberta), and events (typically defined by space-time, like this class session), whether by choice or circumstance.  
* Such affiliations define ''bipartite'' networks comprising two kinds of vertex, which we can call ''actors'' and ''events'' (don't be confused - ''events'' could be more like groups)
+
* Such affiliations define ''bipartite'' networks comprising two kinds of vertex, which we can call ''actors'' and ''events'' (don't be confused - ''events'' could be more like groups).
 
* In a ''bipartite'' network there are two kinds of vertex, type A and type B.  All lines connect a type A vertex to a type B vertex - there are no direct connections between vertices of type A, nor are there direct connections between vertices of type B.  
 
* In a ''bipartite'' network there are two kinds of vertex, type A and type B.  All lines connect a type A vertex to a type B vertex - there are no direct connections between vertices of type A, nor are there direct connections between vertices of type B.  
 
* A bipartite network is also called "two mode", since there are two kinds of vertex, and is represented by a matrix rectangle rather than a square (see this in Excel)
 
* A bipartite network is also called "two mode", since there are two kinds of vertex, and is represented by a matrix rectangle rather than a square (see this in Excel)
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** Note:  social identity can't be captured in a single Pajek partition....why?  The concept of partition is closer to the traditional "culture" model of exclusive all-encompassing identities.
 
** Note:  social identity can't be captured in a single Pajek partition....why?  The concept of partition is closer to the traditional "culture" model of exclusive all-encompassing identities.
 
* Social circles may also imply ''power circles'' with critical implications for relationships among "events" (groups).  Example:  [http://www.theyrule.net/ Interlocking directorates]
 
* Social circles may also imply ''power circles'' with critical implications for relationships among "events" (groups).  Example:  [http://www.theyrule.net/ Interlocking directorates]
* Typical  assumptions about affiliation networks (critique! test!) (see p. 101):
+
* Degree of a vertex indicates the scope of the corresponding social circle:
 +
** Degree of an event:  ''size'' of the event
 +
** Degree of an actor:  ''rate of participation'' of the actor
 +
 
 +
=== Typical  assumptions about affiliation networks ===
 +
* Book states them as facts (see p. 101), but you should ''critique them in theory! test them in your projects!''
 
# Affiliations are institutional or structural -  less personal than friendships or sentiments.  [What do you think? How could we test this?]
 
# Affiliations are institutional or structural -  less personal than friendships or sentiments.  [What do you think? How could we test this?]
 
# "Although membership lists do not tell us exactly which people interact, communicate, and like each other, we may assume that there is a fair chance that they will." [what factors might impact the chances of actual dyadic interaction?]
 
# "Although membership lists do not tell us exactly which people interact, communicate, and like each other, we may assume that there is a fair chance that they will." [what factors might impact the chances of actual dyadic interaction?]
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## enable indirect communication/control between the circles as a whole.
 
## enable indirect communication/control between the circles as a whole.
 
# "Joint membership in a social circle often entails similarities in other social domains."  (i.e. ''homophily'' principle...Cause or effect?)
 
# "Joint membership in a social circle often entails similarities in other social domains."  (i.e. ''homophily'' principle...Cause or effect?)
* Representing two-mode networks with rectangular matrices
+
=== [https://docs.google.com/spreadsheet/ccc?key=0AixxqMLmpQLVdHk1MEFHMTFHaDlIMjQzSWRuZ01JRlE Matrix Representations] ===
 +
* One-mode networks are naturally represented using
 +
** upper triangular matrix, no diagonal (undirected simple)
 +
** upper triangular matrix (undirected with loops)
 +
** square matrix (directed with loops)
 +
* Two-mode networks are naturally represented using rectangular matrices
 
** Rows represent first mode (e.g. actors)
 
** Rows represent first mode (e.g. actors)
 
** Columns represent second mode (e.g. events)
 
** Columns represent second mode (e.g. events)
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** One-mode network derived from rows (e.g. actors)
 
** One-mode network derived from rows (e.g. actors)
 
** One-mode network derived from columns (e.g. events)
 
** One-mode network derived from columns (e.g. events)
 +
* Representing two-mode networks with lists of edges
 +
** Simply listing edges may violate condition that actors can't link to actors, or events to events
 +
** Thus we must also provide a means of identifying which vertices are rows (or, conversely, which vertices are columns)
  
 
== Applications:  creating and manipulating two mode networks ==
 
== Applications:  creating and manipulating two mode networks ==
* using txt2pajek to generate a [[sample two-mode network]]
+
* Two-mode network in Pajek
* Pajek and Scotland.paj
+
** Vertex command is followed by two numbers:  (a) the number of vertices; (b) the number of rows (whether actors or events)
== Line values ==
+
** When Pajek sees two numbers instead of one, it generates an ''affiliation partition'' to match.
 +
* Using [http://www.pfeffer.at/txt2pajek/ txt2pajek] to generate a [[sample two-mode network]]
 +
===  Corporate interlocks in Scotland, 1904-5 ===
 +
* Early 20th century: joint stock companies began to form
 +
** owned by shareholders
 +
** represented by boards of directors
 +
* Interlocking directorates linked the companies (and companies linked the directors)
 +
* Data: 136 multiple directors for 108 largest joint stock companies, of various types:
 +
** non-financial firms (64)
 +
** banks (8)
 +
** insurance companies (14)
 +
** investment and property companies (22)
 +
* Partition:  indicates industry type
 +
# oil & mining
 +
# railway
 +
# engineering & steel
 +
# electricity & chemicals
 +
# domestic products
 +
# banks
 +
# insurance
 +
# investment
 +
* Vector:  indicates total capital in 1,000 pounds sterling
 +
=== Analyzing Scotland.paj ===
 +
==== Two mode net ====
 +
* Info->network
 +
** Number of vertices
 +
** Number of lines
 +
* Affiliation partition separates firms and directors (examine)
 +
* Drawing and energizing. Note bipartite property.
 +
* Degree partition (size of events and rates of participation), can be displayed as vertex size (convert to vector)
 +
* Components
 +
 
 +
====One mode nets ====
 +
* Derived networks: Each two-mode network induces two one-mode networks:  (a) by events (groups), (b) by actors, as follows:
 +
** By events (groups):  events are linked by one line per shared actor
 +
** By actors: actors are linked by one line per shared event (group)
 +
** Note:  loops represent size of events, participation rates of actors:
 +
*** each event (group) shares each actor with ''itself'', so each actor induces a loop for every event in which it participates
 +
*** each actor shares each event (group) with ''itself'', so each event induces a loop for every actor participating in it
 +
* Derived networks are typically not simple, but one can replace multiple lines by a single line with value = number of lines replaced. This value is called ''line multiplicity'' and the resulting network is called a ''valued network''.
 +
* We can convert Scotland.net into one-mode network of firms (no loops, no multiple lines).
 +
** View line values (info->network->line values)
 +
** Add degree information from the original network (create a degree partition, then extract using the affiliation partition)
 +
** m-slices
 +
*** display 2-slice
 +
*** valued core

Latest revision as of 08:19, 8 October 2019

Quiz #2 take 2

  • A pedagogical success. Nearly everyone did much better than before.
  • page 1 - bravo! (perhaps one or two arithmetic mistakes, or creating a semiwalk that was also a semipath...)
  • page 2, also bravo, mostly - but a few common misconceptions remain:
    • components can't overlap (because they're maximal)
    • cores: can't be determined from degree. For one thing, a vertex in the 4-core has to be connected to at least 4 others in the 4-core (by definition!). Therefore the smallest 4-core will have 5 vertices. Some people indicated a single node as belonging to the 4-core.
    • cliques: are defined to be maximal. So a triad isn't necessarily a clique, though if it's not a clique on its own it must be part of a larger clique. Note also that a square is not a clique unless it contains its diagonals.

4.8

  • How to define the flying teams?

Chapter 5: Affiliation networks

Concepts

Basic ideas

  • People affiliate to groups (often defined by space, like the University of Alberta), and events (typically defined by space-time, like this class session), whether by choice or circumstance.
  • Such affiliations define bipartite networks comprising two kinds of vertex, which we can call actors and events (don't be confused - events could be more like groups).
  • In a bipartite network there are two kinds of vertex, type A and type B. All lines connect a type A vertex to a type B vertex - there are no direct connections between vertices of type A, nor are there direct connections between vertices of type B.
  • A bipartite network is also called "two mode", since there are two kinds of vertex, and is represented by a matrix rectangle rather than a square (see this in Excel)
  • Affiliations define social circles which overlap.
  • Network representation of identity as a model for social belonging:
    • Culture model (common in traditional ethnomusicology): each individual belongs to one "complex whole" as Tylor put it in 1847.
    • Identity model (more common in sociology and contemporary ethnomusicology): each individual associates with multiple "simple parts", each person in a slightly different way. These "parts" can be viewed as social circles whose intersection is the individual.
    • Note: social identity can't be captured in a single Pajek partition....why? The concept of partition is closer to the traditional "culture" model of exclusive all-encompassing identities.
  • Social circles may also imply power circles with critical implications for relationships among "events" (groups). Example: Interlocking directorates
  • Degree of a vertex indicates the scope of the corresponding social circle:
    • Degree of an event: size of the event
    • Degree of an actor: rate of participation of the actor

Typical assumptions about affiliation networks

  • Book states them as facts (see p. 101), but you should critique them in theory! test them in your projects!
  1. Affiliations are institutional or structural - less personal than friendships or sentiments. [What do you think? How could we test this?]
  2. "Although membership lists do not tell us exactly which people interact, communicate, and like each other, we may assume that there is a fair chance that they will." [what factors might impact the chances of actual dyadic interaction?]
  3. Actors at the intersection of multiple social circles...
    1. tend to interact even more
    2. enable indirect communication/control between the circles as a whole.
  4. "Joint membership in a social circle often entails similarities in other social domains." (i.e. homophily principle...Cause or effect?)

Matrix Representations

  • One-mode networks are naturally represented using
    • upper triangular matrix, no diagonal (undirected simple)
    • upper triangular matrix (undirected with loops)
    • square matrix (directed with loops)
  • Two-mode networks are naturally represented using rectangular matrices
    • Rows represent first mode (e.g. actors)
    • Columns represent second mode (e.g. events)
  • Deriving one-mode network from two-mode network.
    • Mapping the "hidden networks" implied by two-mode network (under assumptions above) can be highly significant
    • One-mode network derived from rows (e.g. actors)
    • One-mode network derived from columns (e.g. events)
  • Representing two-mode networks with lists of edges
    • Simply listing edges may violate condition that actors can't link to actors, or events to events
    • Thus we must also provide a means of identifying which vertices are rows (or, conversely, which vertices are columns)

Applications: creating and manipulating two mode networks

  • Two-mode network in Pajek
    • Vertex command is followed by two numbers: (a) the number of vertices; (b) the number of rows (whether actors or events)
    • When Pajek sees two numbers instead of one, it generates an affiliation partition to match.
  • Using txt2pajek to generate a sample two-mode network

Corporate interlocks in Scotland, 1904-5

  • Early 20th century: joint stock companies began to form
    • owned by shareholders
    • represented by boards of directors
  • Interlocking directorates linked the companies (and companies linked the directors)
  • Data: 136 multiple directors for 108 largest joint stock companies, of various types:
    • non-financial firms (64)
    • banks (8)
    • insurance companies (14)
    • investment and property companies (22)
  • Partition: indicates industry type
  1. oil & mining
  2. railway
  3. engineering & steel
  4. electricity & chemicals
  5. domestic products
  6. banks
  7. insurance
  8. investment
  • Vector: indicates total capital in 1,000 pounds sterling

Analyzing Scotland.paj

Two mode net

  • Info->network
    • Number of vertices
    • Number of lines
  • Affiliation partition separates firms and directors (examine)
  • Drawing and energizing. Note bipartite property.
  • Degree partition (size of events and rates of participation), can be displayed as vertex size (convert to vector)
  • Components

One mode nets

  • Derived networks: Each two-mode network induces two one-mode networks: (a) by events (groups), (b) by actors, as follows:
    • By events (groups): events are linked by one line per shared actor
    • By actors: actors are linked by one line per shared event (group)
    • Note: loops represent size of events, participation rates of actors:
      • each event (group) shares each actor with itself, so each actor induces a loop for every event in which it participates
      • each actor shares each event (group) with itself, so each event induces a loop for every actor participating in it
  • Derived networks are typically not simple, but one can replace multiple lines by a single line with value = number of lines replaced. This value is called line multiplicity and the resulting network is called a valued network.
  • We can convert Scotland.net into one-mode network of firms (no loops, no multiple lines).
    • View line values (info->network->line values)
    • Add degree information from the original network (create a degree partition, then extract using the affiliation partition)
    • m-slices
      • display 2-slice
      • valued core