SOME STATISTICAL PHYSICS METHODS FOR INVESTIGATIONS OF COMPLEX NETWORKS AND THEIR BACKGROUND

This paper presentsthe physics backgrounds, history of development, viewpoints andmethods of some statistical physics methods recently used incomplex network investigations (mean field theory, masterequation, rate equation, and generating function). We reviewed howthe mean field theory was developed and used in the studies ofcontinuous phase transition, self-organized criticality andepidemics, and how the mean field theory ideas and methods evolvedin the transition from equilibrium to non-equilibrium studies. Thecorresponding physics ideas and methods of master equation, rateequation, and generating function are first presented, and somecomplex network research achievements obtained by using themethods are reviewed in the last section, such as using mean fieldmethods, master equation and rate equation to solve the mostfamous and other noticeable network evolution models, to solvesome network statistical properties and to analyze thecharacteristic descriptions of some network physical processes.