3) Partitioning a network of US political blogs. In this problem we will study a network of Internet blogs on the subject of US politics, with the goal of partitioning the graph into liberal (i.e., Democrat) and conservative (i.e., Republican) blogger communities. Data on the 2004 US Elections political blogosphere was compiled by L. Adamic and N. Glance in 2005, and can be obtained e.g., from Mark Newmans network collection at http://www-personal. umich.edu/mejn/netdata/. Here we use an undirected version of the original directed graph, where edges correspond to hyperlinks between blogs. The network comprises Nv = 1490 blogs (vertices), and a binary attribute associated to each vertex indicates political leaning according to: 0 (liberal) and 1 (conservative). A) Download the political blogosphere dataset political blogs.mat. B) Compute the degrees dv of all nodes v V and the total number of edges Ne. Hence compute the modularity matrix Bfor the network. C) Implement the spectral modularity maximization algorithm to perform a bisection of the graph, i.e., split the vertices into two communities.