Difference between revisions of "MCSN Tuesday, 1-Nov-11"
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** When Pajek sees two numbers instead of one, it generates an ''affiliation partition'' to match. | ** When Pajek sees two numbers instead of one, it generates an ''affiliation partition'' to match. | ||
* Using txt2pajek to generate a [[sample two-mode network]] | * 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 | ||
+ | # oil& mining | ||
+ | # railway | ||
+ | # engineering & steel | ||
+ | # electricity & chemicals | ||
+ | # domestic products | ||
+ | # banks | ||
+ | # insurance | ||
+ | # investment | ||
+ | ** Vector: indicates total capital in 1,000 pounds sterling | ||
+ | |||
== Line values == | == Line values == |
Revision as of 09:57, 1 November 2011
Contents
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?
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
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?]
- "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?]
- Actors at the intersection of multiple social circles...
- tend to interact even more
- 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?)
Representations
- 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)
- 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
- Early 20th century: joint stock companies began to form
- oil& mining
- railway
- engineering & steel
- electricity & chemicals
- domestic products
- banks
- insurance
- investment
- Vector: indicates total capital in 1,000 pounds sterling