MCSN Tuesday, 1-Nov-11

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

• using txt2pajek to generate a sample two-mode network
• Pajek and Scotland.paj