Spectral analysis for gene communities in cancer cells

Abstract

We investigate gene interaction networks in various cancer cells by spectral analysis of the adjacency matrices. We observe localization of the networks on hub genes which have extraordinarily many links. The eigenvector centralities take finite values only on special nodes when the hub degree exceeds a critical value $d_c\simeq 40$. The degree correlation function shows the disassortative behavior in the large degrees, and the nodes whose degrees $d\gtrsim 40$ have tendencies to link to small degree nodes. The communities of the gene networks centered at the hub genes are extracted by the amount of node degree discrepancies between linked nodes. We verify the Wigner-Dyson distribution of the nearest neighbor eigenvalues spacing distribution $P(s)$ in the small degree discrepancy communities, and the Poisson $P(s)$ in the communities of large degree discrepancies including the hubs.

arXiv comment15 pages, 7 figures, 1 table

References in corpus (15)

• Statistical mechanics of complex networks
• Assortative mixing in networks
• Finding community structure in networks using the eigenvectors of matrices
• Mixing patterns in networks
• Characterization of complex networks: A survey of measurements
• Random Matrix Theories in Quantum Physics: Common Concepts
• Dynamical and correlation properties of the Internet
• Localization and centrality in networks
• Spectra of complex networks
• Modularity and Extreme Edges of the Internet
• Spectra of Sparse Random Matrices
• Spectra of random graphs with arbitrary expected degrees
• Diffusion on Complex Networks : A way to probe their large scale topological structures
• Random matrix analysis for gene interaction networks in cancer cells
• Assortative and disassortative mixing investigated using the spectra of graphs