2. Consider a bipartite graph with two types of nodes, X-nodes and Y- nodes. Let A be its adjacency matrix. (a) Describe

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2 Consider A Bipartite Graph With Two Types Of Nodes X Nodes And Y Nodes Let A Be Its Adjacency Matrix A Describe 1 (50.78 KiB) Viewed 124 times

2. Consider a bipartite graph with two types of nodes, X-nodes and Y- nodes. Let A be its adjacency matrix. (a) Describe the weights in the X projection, say between X-nodes u and v, in terms of the number of 2-step paths between nodes u and v. (b) Hence or otherwise show how the adjacency matrix of the X pro- jection can be obtained from the matrix A2 and the diagonal matrix D with entries ku (the degrees of the nodes in A). Note that the X projection is a weighted graph containing X-nodes only. (c) Consider Topic 2 Slide 5, with the network depicting past records of purchases, with X denoting items bought and Y denoting cus- tomer. Assume that we have a new customer and he buys item X3. You are asked to recommend one item to this customer. Which item will you recommend? Why?