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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 Raders 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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