Spectral analysis for gene communities in cancer cells

TL;DR

This paper uses spectral analysis to study gene interaction networks in cancer cells, revealing hub localization, community structures, and eigenvalue distributions that depend on node degree discrepancies.

Contribution

It introduces a spectral analysis approach to identify gene communities and hub effects in cancer cell networks, highlighting degree-based community distinctions.

Findings

Localization of networks on hub genes with high degrees

Eigenvector centralities concentrate on specific nodes beyond a critical degree

Different eigenvalue spacing distributions characterize communities with varying degree discrepancies

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.