Figure 1 shows a social network of users as nodes that are connected by friendship edges....

 

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Figure 1 shows a social network of users as nodes that are connected by friendship edges. It is important to analyze the community structures of social networks. (a) A strongly connected component can be regarded as a community. Please list all strongly connected components in Figure 1. [6 marks] (b) Given node c in the graph of Figure 1, define the local community of c as the set of nodes with top-3 highest personalized PageRank with respect to c in the graph (the local community includes c itself). Explain the rationale of this local community definition. [4 marks] (c) Based on the local community definition above, with damping factor 0.9, use BCA algorithm in 3 steps to find the local community of node c in the graph of Figure 1. Within a step of BCA, if there are multiple nodes to process, process the nodes in alphabetical order. Please provide the results after each step of BCA and finally show the local community of c. (Keep values in 4 decimal places.) [10 marks] Figure 1 A Social Network Graph with Nodes Connected By Friendship Edges Figure 1 shows a social network of users as nodes that are connected by friendship edges. It is important to analyze the community structures of social networks. (a) A strongly connected component can be regarded as a community. Please list all strongly connected components in Figure 1. [6 marks] (b) Given node c in the graph of Figure 1, define the local community of c as the set of nodes with top-3 highest personalized PageRank with respect to c in the graph (the local community includes c itself). Explain the rationale of this local community definition. [4 marks] (c) Based on the local community definition above, with damping factor 0.9, use BCA algorithm in 3 steps to find the local community of node c in the graph of Figure 1. Within a step of BCA, if there are multiple nodes to process, process the nodes in alphabetical order. Please provide the results after each step of BCA and finally show the local community of c. (Keep values in 4 decimal places.) [10 marks] Figure 1 A Social Network Graph with Nodes Connected By Friendship Edges

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a A strongly connected component is a subgraph where there is a path from every node to every other ... View the full answer