Understanding the noise sensitivity of the top eigenvector in sparse random matrices through resampling procedures, exploring the threshold phenomenon and related works. Results highlight the impact of noise on the eigenvector's stability and reliability in statistical analysis.

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The PageRank algorithm plays a crucial role in determining the importance of web pages based on link structures. Jeffrey D. Ullman from Stanford University explains the concept of PageRank using random surfer model and recursive equations, emphasizing the principal eigenvector of the transition matr

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Discover the importance of centrality in social network analysis through measures like Degree Centrality, Eigenvector Centrality, and Katz Centrality. Learn how these metrics identify the most central vertices in a network based on factors such as connections, citations, and influence. Explore the c

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A detailed exploration of functions of matrices, including exponential of a matrix, eigenvector sets, eigenvalues, Jordan-Canonical form, and applications of Taylor series to compute matrix functions like cosine. The content provides a deep dive into spectral mapping, eigenvalues, eigenvectors, and

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