DAT600: Algorithm Theory - Advanced Graph Algorithms - Engineering Assessment Answer

Internal Code: 1AGJID

Engineering Assessment Answer

TASK: Problem-1: Connected Components Find the connected components of the graph shown in the Figure-1 below, using: 1a. The iterative method that involves the power series of the adjacency matrices, and 1b.The quicker Rader’s method that involves the D matrix. By introducing just one more arc (connection) between two nodes, we can unify all the nodes into one connected components. 1c. Name such a connection (there are several options). Problem-2: Graph Clustering 2a. Find the clusters of the graph shown in the Figure-1. 2b. Introduce the arc D->E into the graph, and explain the changes in the number of clusters. Programming project: The MATLAB code provided for clustering does not realize the factor p, for preventing large clusters pulling the other nodes. 2c. Implement p in this code, and see how cluster changes when p is varied from 0 to 1. Could you explain the changes? Problem-3: Network Centrality 3a. Find the network centrality measures (Degree, Betweenness, and Closeness) for the nodes of the graph in the Figure-1. 3b.How do these values change if the graph is an undirected graph?

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