Power-law Correlations of Connectivities in Biomolecular Networks

Complex networks which describe biological systems such as gene regulations and metabolisms indicate several striking statistical properties such as power-law degree distribution P (k)∼k−γ that is a scalefree property and high clustering coefficient, yielding nontrivial interpretations for topologies and signal transductions of the networks [1]. In this report, we forcus on degree correlation k̄nn(k) [3] denotes average degree (number of edges) of nearest neighbors of nodes with degree k to examine features of neighbor connectivities in the networks. We show that various biomolecular networks exhibit conserved correlations of connectivities; the correlations were initially found in the protein-protein interaction and the regulatory networks in yeast [2]. Furthermore, we propoase a growth network model which reproduces the correlations and provides insights into topologies of the biomolecular networks and several evolutionary mechanisms.