The n-node wheel graph Wn consists of a cycle of n- – 1 rim nodes, each linked to a single hub node. A computer network

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The N Node Wheel Graph Wn Consists Of A Cycle Of N 1 Rim Nodes Each Linked To A Single Hub Node A Computer Network 1 (137.9 KiB) Viewed 22 times

The n-node wheel graph Wn consists of a cycle of n- – 1 rim nodes, each linked to a single hub node. A computer network with a +b – 1 nodes is constructed from two wheel graphs, Wa and Wý, by having them share a rim node. For example, here is a picture of the 16-node network constructed from W, and W8: Wa W Let X be the shared node, and H be the hub from Wa, as illustrated. (a) Calculate the closeness centrality of X and H, in terms of a and b. (6 marks) (b) Hence determine when the hub H has greater closeness centrality than the shared node X, giving a condition relating a and b. (3 marks) (c) Now suppose a = 9 and b = 8, as illustrated. Obtain the value of the degree correlation function knn(k) for each distinct node degree in the network. Is the network assortative or disassortative? Justify your answer. (6 marks)