We can detect communities in networks by maximizing modularity 3.1 Show that each row and each column in the modularity matrix B sums to 0, i.e. 3.2 Construct the modularity matrix B for the following graph. Use exact fractions 3.3 Using your favorite numerical software (eg. numpy or scipy linalg) find the eigen- vector of B that corresponds to its largest eigenvalue. No code submission required. 3.4 Divide the network into two clusters using your result from part (c). Draw the two clusters, add node ids, and draw the corresponding dendrogram. We can detect communities in networks by maximizing modularity 3.1 Show that each row and each column in the modularity matrix B sums to 0, i.e. 3.2 Construct the modularity matrix B for the following graph. Use exact fractions 3.3 Using your favorite numerical software (eg. numpy or scipy linalg) find the eigen- vector of B that corresponds to its largest eigenvalue. No code submission required. 3.4 Divide the network into two clusters using your result from part (c). Draw the two clusters, add node ids, and draw the corresponding dendrogram