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 the localization of the networks on hub genes, which have an extraordinary number of links. The eigenvector centralities take finite values only on special nodes when the hub degree exceeds the critical value $d_c \simeq 40$. The degree correlation function shows the disassortative behaviour in the large degrees, and the nodes whose degrees are $d \gtrsim 40$ have a tendency to link to small degree nodes. The communities of the gene networks centred at the hub genes are extracted based on the amount of node degree discrepancies between linked nodes. We verify the Wigner–Dyson distribution of the nearest neighbour eigenvalues spacing distribution $P(s)$ in the small degree discrepancy communities (the assortative communities), and the Poisson $P(s)$ in the communities of large degree discrepancies (the disassortative communities) including the hubs.