Programming excercise

Download NetworkX, a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks. This package has a library of various kinds of graphs as well as the implementation of various useful algorithms for social network analysis. Part 1: The goal of this homework is to generate a social network. Recall how a power-law graph is generated using the idea of preferential attachment. Starting with a single node, in each step, add a node to the network using a single edge. The probability of choosing the node to which it will attach will be proportional to the degree of that node. a. Using this rule, generate three graphs, n = 1000, 2000, 5000 nodes. b. Show the degree distribution of the generated graph: plot logN(k) versus log k, where k is the degree of a node and N(k) is the number of nodes having degree k. Verify that the power law (N(k) = c • k−r) holds, and estimate the value of r. Part 2: Consider the Karate Club network described in [login to view URL] Your tasks are as follows: • a. Compute the edge(s) of highest betweenness in this network. • b. Remove the edge(s) of highest betweenness, and visualize the graph and see if it has been partitioned into disjoint communities. If not, then repeat the earlier two steps, until the graph partitions, and then stop. • c. List the edges that you removed.