## NPTEL Social Network Analysis Week 10 Assignment Answers 2024

1. Let G(V,E) be a graph where V represents the set of vertices and E represents the set of edges. If there is a mapping function defined as f : u → R^{d}, where u is an element of V, what is this mapping function called?

- Random walk
- Edge embedding
- Graph embedding
- Node embedding

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2. Which of the following is not a homogenous network?

- Co-author network
- Actor-Movie network
- Citation network
- Social media user network

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3. A complete graph embedding generally makes sense if we have more than one graph to embed.

- True
- False

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4. The number of features in a machine learning model is often smaller than the raw dataset.

- True
- False

Answer :-

5. What is the fundamental idea behind matrix factorization?

- Increases the dimensionality of data
- Structure-preserving dimensionality reduction
- Data visualization
- None of the above

Answer :-

6. Match the following graph representation of learning methods to their main category:

- Dimensionality Reduction: HOPE, Matrix Factorization: DeepWalk, Random Walk: node2vec, Neural Network Based: GraRep
- Dimensionality Reduction: node2vec, Matrix Factorization: Isometric Feature Mapping, Random Walk: GraRep, Neural Network Based: Kernel Methods
- Dimensionality Reduction: Isometric Feature Mapping, Matrix Factorization: GraRep, Random Walk: node2vec, Neural Network Based: Graph Convolution Network
- Dimensionality Reduction: node2vec, Matrix Factorization: Isometric Feature Mapping, Random Walk: GraRep, Neural Network Based: Graph Convolution Network

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7. How does the space complexity of representing a graph using its adjacency matrix change with an increase in the number of nodes?

- increases linearly with the number of nodes
- increases polynomially with the number of nodes
- increases exponentially with the number of nodes
- remains constant

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8. What do the matrices U and V represent in the Singular Value Decomposition (SVD) of a matrix A=USVT?

- U contains the right singular vectors, and V contains the left singular vectors.
- Both U and V contain the same singular vectors.
- U contains the left singular vectors, and V contains the right singular vectors.
- U and V represent the original matrix A directly.

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9. In GraRep, for a network G(V,E) and its adjacency matrix A. The transition probability of moving from node w to node c in exactly k-steps is given by:

- p
_{k}(c|w) = A^{k}_{w,c} - p
_{k}(w|c) = A^{k}_{w,c} - p
_{k}(c|w) = A^{kc,w} - p
_{k}(w|c) = A^{k}_{c,w}

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10. Negative sampling helps in:

- Reducing the computation on positive samples.
- Reducing the computation on negative samples.
- Reducing the computation on both positive and negative samples
- No reduction in computation is obtained.

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