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Abstract: We analyze gene co-expression network under the random matrix theoryframework. The nearest neighbor spacing distribution of the adjacency matrix ofthis network follows Gaussian orthogonal statistics of random matrix theoryRMT. Spectral rigidity test follows random matrix prediction for a certainrange, and deviates after wards. Eigenvector analysis of the network usinginverse participation ratio IPR suggests that the statistics of bulk of theeigenvalues of network is consistent with those of the real symmetric randommatrix, whereas few eigenvalues are localized. Based on these IPR calculations,we can divide eigenvalues in three sets; A The non-degenerate part thatfollows RMT. B The non-degenerate part, at both ends and at intermediateeigenvalues, which deviate from RMT and expected to contain information about{\it important nodes} in the network. C The degenerate part with $zero$eigenvalue, which fluctuates around RMT predicted value. We identify nodescorresponding to the dominant modes of the corresponding eigenvectors andanalyze their structural properties.



Author: Sarika Jalan, Norbert Solymosi, Gabör Vattay, Baowen Li

Source: https://arxiv.org/







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