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.
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