Homeworks

Solve the exercise in the attached file Homework Fig. 2.4 (from the book by Kolaczyk, 2009, pp. 45-46)

Please add a text with the solutions and some discussion. 

Let consider the following two datasets

data(aidsblog) and data(yeast) 

Note that aidsblog is contained in the sand package (so run library(sand) to load it with the command data(aidsblog) ) 

Yeast is contained in the igraphdata package (so run library(igraphdata) to load it with the command data(yeast) )

According to the nature of the data:

1) compute and comment some global network statistics (including size, number of edges, and diameter, please refer for instance to the example of co-authorship in the data collection slides)

2) if needed decompose the network into distinct components

3) compute some centrality scores for the individual vertices

4) extract the ego-network the most central vertex according to at east 2 centrality score (e.g., degree and closeness) and compute and comment the local clustering coefficient 

Please deliver an R script containing both your code and comments by April 19th possibly.

Considering the fblog data (it's in the "sand" library and it is a snapshot of the network of interactions in a single day of October 2006 among political blogs in France) produce a R file reporting the codes for the following tasks:

5) choose 2 political parties (say P1 and P2) and plot the network of blogs beloging to the chosen parties using different colors for intra links (P1 <--> P1 and P2 <--> P2) and for interlinks (P1<-->P2)

1) Try to use some igraph functions to produce a graph like the caveman graph (see slides on community detection #2)

Using the graph of the point 1 do the following exercises:

2) Choose the value k and use the pruning algorithm to detect the cliques of size k (see slides community detection #1, from slides 10 on)

3) Perform a k-core decomposition and produce the hierarchical plot using the appropriate plot 

4) obtain the MDS coordinates following the approach from the slides (see community detection #2, slide 7 on)

5) Compute the initial value of the modularity if all nodes were placed in distinct communities

6) Run the Louvain algorithm with the built-in igraph function

7) Implement Newman-Girvan on the same graph and check if you obtain the same solution of the Louvain algorithm

Please, deliver only the commented R script (no need to upload pictures) possibly by the end of the week.