Extreme self-organization in networks constructed from gene expression data

TL;DR

This paper investigates gene expression networks from various cancers, revealing that they exhibit extreme self-organization characterized by power-law degree distributions, small-world properties, and implications for evolutionary biology.

Contribution

The study introduces an order parameter to analyze network homogeneity and demonstrates power-law degree distributions and small-world behavior in gene expression networks.

Findings

Networks show power-law degree distribution with exponent ~1.

Eigenvalue spectra indicate small-world properties.

Results suggest self-organized criticality in gene networks.

Abstract

We study networks constructed from gene expression data obtained from many types of cancers. The networks are constructed by connecting vertices that belong to each others' list of K-nearest-neighbors, with K being an a priori selected non-negative integer. We introduce an order parameter for characterizing the homogeneity of the networks. On minimizing the order parameter with respect to K, degree distribution of the networks shows power-law behavior in the tails with an exponent of unity. Analysis of the eigenvalue spectrum of the networks confirms the presence of the power-law and small-world behavior. We discuss the significance of these findings in the context of evolutionary biological processes.