NPTEL Social Networks Week 8 Assignment Answers 2025
1. In the context of hubs and authorities, what is the primary role of a hub in a network?
- It points to many authoritative nodes.
- It is referenced by multiple other hubs.
- It has the highest in-degree in the graph
- It acts as a standalone influencer without dependencies.
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2. Which of the following best describes the relationship between hubs and authorities in a network?
- Authorities point to hubs.
- Hubs and authorities are disconnected groups.
- Hubs reinforce the value of authorities by linking to them.
- Hubs only exist in undirected graphs
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3. What is the key idea behind the principle of repeated improvements in link analysis?
- Incrementally refining scores for nodes by iterating calculations.
- Using random assignments to simulate diffusion in the network.
- Combining the scores of hubs and authorities without iteration.
- Calculating scores only once based on initial graph structure.
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4. What happens to the hub and authority scores of nodes after several iterations of the HITS algorithm?
- They converge to stable values.
- They oscillate indefinitely
- They reset to their initial values.
- They grow without bound.
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5. Which algorithm is commonly used to calculate hub and authority scores in a graph?
- HITS (Hyperlink-Induced Topic Search)
- PageRank
- Dijkstra’s Algorithm
- Breadth-First Search
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6. In the HITS algorithm, how are hub and authority scores updated during each iteration?
- Hub scores are calculated based on outgoing links, and authority scores are based on incoming links.
- Hub scores are assigned randomly, and authority scores depend on the graph density.
- Hub and authority scores are not interdependent.
- Hub and authority scores are calculated independently of the adjacency matrix.
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7. What ensures the convergence of the PageRank algorithm during iterative updates?
- The graph is strongly connected, and a damping factor is used.
- All nodes are assigned equal rank initially.
- Only the top-ranked nodes are considered for convergence.
- The damping factor is set to zero.
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8. How does PageRank ensure conservation of rank across the graph?
- By redistributing rank proportionally across outgoing edges.
- By normalizing scores at each step of the iteration.
- By removing nodes with zero in-degree.
- By assigning higher scores to isolated nodes.
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9. Why does repeated multiplication of a transition matrix in PageRank lead to convergence?
- The matrix represents a stochastic process that stabilizes over time.
- The matrix has uniform eigenvalues that dictate convergence.
- The graph contains no cycles, ensuring convergence.
- The damping factor eliminates randomness in the network.
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10. In the context of PageRank, what is the significance of the dominant eigenvector of the transition matrix?
- It represents the steady-state distribution of PageRank scores.
- It determines the degree distribution of nodes in the graph.
- It is used to calculate the number of edges in the graph.
- It is irrelevant for networks with isolated nodes.
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