Approximations of centrality scores Sample Clauses

Approximations of centrality scores. In this section, we will provide an overview of two iterative methods used in this thesis to approximate centrality measures based on matrix functions. The matrix exponential and resolvent are computationally expensive and exact computations are not possible for large networks. Several approaches are available for computing the matrix ex- ponential [65]. A commonly used scheme is the one based on Padé approximation combined with the scaling and squaring method [64, 65], implemented in Matlab by the expm function. For an n × n matrix, this method requires O(n2) storage and O(n3) arithmetic operations; current implementations are geared toward small, dense matri- ces. Evaluation of the matrix exponential based on diagonalization also requiresO(n2) storage and O(n3) operations. Furthermore, these methods cannot be easily adapted to the case where only selected entries (e.g., the diagonal ones) of the matrix exponential are of interest.
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