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

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* 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)
* Affiliations define ''social circles'' which overlap.
+
* Affiliations define ''social circles'' which overlap.  
 
* Network representation of ''identity'' as a model for social belonging:
 
* Network representation of ''identity'' as a model for social belonging:
 
** Culture model (common in traditional ethnomusicology):  each individual belongs to one "complex whole" as [https://secure.wikimedia.org/wikipedia/en/wiki/Edward_Burnett_Tylor#Ideology_and_.22Primitive_Culture.22 Tylor] put it in 1847.
 
** Culture model (common in traditional ethnomusicology):  each individual belongs to one "complex whole" as [https://secure.wikimedia.org/wikipedia/en/wiki/Edward_Burnett_Tylor#Ideology_and_.22Primitive_Culture.22 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.
 
** 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.
 
** 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.
* 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):
 
* Typical  assumptions about affiliation networks (critique! test!) (see p. 101):
 
# 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?]
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# Actors at the intersection of ''multiple'' social circles...
 
# Actors at the intersection of ''multiple'' social circles...
 
## tend to interact even more
 
## tend to interact even more
## enable indirect communication 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
 
* Representing two-mode networks with 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)
* Deriving one-mode from two-mode
+
* Deriving one-mode network from two-mode network.
** Derived from rows
+
** Mapping  the "hidden networks" implied by two-mode network (under assumptions above) can be highly significant
** Derived from columns
+
** One-mode network derived from rows (e.g. actors)
 +
** One-mode network derived from columns (e.g. events)
 +
 
 
== Practice with two mode networks ==
 
== Practice with two mode networks ==
 
* using txt2pajek to generate a [[sample two-mode network]]
 
* using txt2pajek to generate a [[sample two-mode network]]
 
* Pajek and Scotland.paj
 
* Pajek and Scotland.paj
 
== Line values ==
 
== Line values ==

Revision as of 08:26, 1 November 2011

Quiz

  • Success! Nearly everyone did much better than before.
  • page 1 - bravo!
  • page 2, mainly bravo, 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?

Affiliation networks

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
  • Typical assumptions about affiliation networks (critique! test!) (see p. 101):
  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?)
  • Representing two-mode networks with 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)

Practice with two mode networks

Line values