Difference between revisions of "MCSN Tuesday, 1-Nov-11"
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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 = |
== Concepts == | == Concepts == | ||
=== Basic ideas === | === 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) | ||
Line 22: | Line 22: | ||
** 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] | ||
+ | * 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 === | === 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!'' | * Book states them as facts (see p. 101), but you should ''critique them in theory! test them in your projects!'' | ||
Line 30: | Line 34: | ||
## 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?) | ||
− | === Representations === | + | === [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) | ||
Line 46: | Line 54: | ||
** Vertex command is followed by two numbers: (a) the number of vertices; (b) the number of rows (whether actors or events) | ** 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. | ** 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 [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 | # oil & mining | ||
# railway | # railway | ||
Line 66: | Line 74: | ||
# insurance | # insurance | ||
# investment | # 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 09:19, 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!
- 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?)
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
- 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