Graphs as Models of Scale-Free Networks

In bioinformatics research field, researchers from biology, and physics, mathematics, computer science and other disciplines explore the mystery of genetic language by the combination of experimental researches and theoretical analysis, and try reveals the essence of biological genetic information. Bollobás and Riordan pointed out that the definition of scale-free in the context of network graph models has never been made precise. We use spanning trees and other graphs to illustrate some results and phenomenon and try expressing mathematically key notions from researching scale-free networks, and explore constructions and operations of complex networks.