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.

• Received 31 July 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.268702