Principal Component Centrality
Let X denote the N x N matrix of concatenated eigenvectors X = [X1X2 ... XN] and let Λ = [λ1,λ2 ... λN]' be the vector of eigenvalues. Furthermore, if P < N and if matrix X has dimensions N x N , then XNxP will denote the submatrix of X consisting of the first N rows and first P columns. Then PCC can be expressed in matrix form as:
PCC is a measure of node centrality and is based on PCA and the Karhunen Loeve transform (KLT) which takes the view of treating a graphs adjacency matrix as a covariance matrix.
Unlike eigenvector centrality, PCC allows the addition of more features for the computation of node centralities.
Weighted Principal Component Centrality
Li, J.R., YU, L. and ZHAO, J., 2014. A Node Centrality Evaluation Model for Weighted Social Networks. Journal of University of Electronic Science and Technology of China, 43(3), pp.322-328.
- ILYAS, M. U. & RADHA, H. A KLT-inspired node centrality for identifying influential neighborhoods in graphs. Information Sciences and Systems (CISS), 2010 44th Annual Conference on, 17-19 March 2010 2010. 1-7.
Wonderful work, I have been searching all over the internet on principal component centrality computation and here it is in your website. kindly assist me on how to implement this particalar centrality using either the centiserver or centiserve please, my email address is firstname.lastname@example.org. I look forward to hearing from you soon. Thank you.
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