K-Terminal Network Permutation Importance Measure Based on Mixture C-Spectrum

The construction spectrum(C-spectrum) is often used to exploit the network reliability and importance measure. It depends only on the network structure and hence called structure invariant. Importance measure can be used to quantify the criticality of edge within a network. This paper aim at generalizing the traditional permutation importance measure to accommodate the case of K-terminal network in which all the edges fail with independent and equal probability. A concept for mixture C-spectrum is introduced to evaluate the permutation importance measure of edges. It is proved that the rankings according to the permutation importance measure depend only on the network structure through the mixture C-spectrum when the network has special structure or the reliability of edge is sufficient large. Finally, numerical experiment show that the Monte Carlo algorithm based on the mixture C-spectrum can be efficiently used to evaluate the permutation importance measure.