Difference between revisions of "MCSN Tuesday, 25-Oct-11"
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− | * Review of quiz and concepts | + | |
+ | * Note: | ||
+ | ** Repeat quiz on Thursday, either to replace or average with last quiz (your choice) | ||
+ | ** Draft proposals are also due Thursday | ||
+ | ** 4.8 due today | ||
+ | ** Open Quiz#2.paj | ||
+ | |||
+ | ---- | ||
+ | |||
+ | * Review of quiz and chapter 3 concepts | ||
+ | ** ''It's very important that you understand this material! Please see me if you do not.'' | ||
** Density | ** Density | ||
*** # lines divided by # possible lines | *** # lines divided by # possible lines | ||
Line 50: | Line 60: | ||
*** Cliques need not cover the network | *** Cliques need not cover the network | ||
*** Cliques generally do not form a partition | *** Cliques generally do not form a partition | ||
+ | * Balance and cluster theory (ch 4) |
Revision as of 10:01, 25 October 2011
- Note:
- Repeat quiz on Thursday, either to replace or average with last quiz (your choice)
- Draft proposals are also due Thursday
- 4.8 due today
- Open Quiz#2.paj
- Review of quiz and chapter 3 concepts
- It's very important that you understand this material! Please see me if you do not.
- Density
- # lines divided by # possible lines
- Cannot exceed 100%
- Degree
- indegree and outdegree
- total degree: sum over all vertices
- average degree...
- ...and a neat trick for computing total and average degree (e.g. if all you know is there are 8 vertices and 8 lines...)
- Components
- criteria: (a) violate no one-way streets; (b) do not visit any vertex twice.
- path (a,b)
- semipath (not a, b)
- walk (a, not b)
- semiwalk (not a, not b)
- weak
- a subnet is weakly connected if each pair of vertices is connected by a semipath
- a weak component is a maximal weakly connected subnet
- find it by tracing all the vertices semipath-reachable from a particular vertex V
- strong
- a subnet is strongly connected if each pair of vertices is connected by a path
- a strong component is a maximal strongly connected subnet
- find it by tracing all the vertices path-reachable from a particular vertex V, which can also reach V
- components never overlap
- components cover the network
- components therefore define a partition
- Giant component formation
- Play with Pajek: 100 vertices, vary the number of arcs. How many components are there? How big are they? You'll notice with more than 100 arcs that a large component arises.
- Try this beautiful simulation which illustrates giant component formation in a random graph.
- criteria: (a) violate no one-way streets; (b) do not visit any vertex twice.
- K-cores
- The k-core is a maximal subnet in which every vertex is degree k or greater.
- k-cores "nest": the 0-core contains the 1-core, which contains the 2-core, which contains the 3-core
- k-cores are not necessarily connected
- a partition is defined by assigning each vertex to its maximum k-core.
- this partition cannot be computed from degree information alone!
- find the k-core by locating a vertex of degree k or more, then checking if at least k neighbors could be included in the k-core.
- OR: find the k-core by deleting vertices of degree less than k, then repeating.
- Complete networks, triads and cliques
- Complete networks
- A complete network is 100% dense
- A complete triad is a triangular complete network ("bone")
- Complete triads may overlap
- The set of complete triads ("skeleton") may have several components
- Each component is considered a "social circle"
- Complete triads do not form a partition
- A partition can be generated by counting, for each vertex, how many triads include it
- Cliques
- A clique is a maximal complete subnetwork
- Cliques may overlap
- Cliques need not cover the network
- Cliques generally do not form a partition
- Complete networks
- Balance and cluster theory (ch 4)