Random network assignment

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Random network assignment

Use Pajek to create a series of 8 networks using the command:

Network -> Create Random Network -> Bernoulli/Poisson -> Undirected -> General

All networks should contain 1000 vertices. Set network average degree for the 8 networks as follows:

  1. Average degree 0.5
  2. Average degree 1.0
  3. Average degree 1.5
  4. Average degree 2.0
  5. Average degree 2.5
  6. Average degree 3.0
  7. Average degree 3.5
  8. Average degree 4.0

Create a spreadsheet with the following column headings:

  1. Average degree
  2. Size of the largest component
  3. Size of the 1-core
  4. Size of the 2-core
  5. Size of the 3-core

(You'll use Network -> Create Partition -> Components -> Weak to determine the size of the largest component, and Network -> Create Partition -> Components -> k-Core -> Input to determine the sizes of the components. NOte that if there is no k-core listed for a particular size, it means that k-core contains no nodes.)

Then create a scatter plot chart using this data (connect the dots with lines). What patterns do you see?

(Note that Pajek places a node in its highest k-core. This is why a particular k-core will grow and then shrink again - as more nodes enter higher cores.)

If you have time, try extracting the higher cores from some of these networks. You may also try running one of the network experiments several times to check on how much variation there is in the component and k-core sizes.