Introduction to Micro Life of Graphs. I

Abstract

Multiparticle systems on complicated metric graphs might have many applications in physics, biology and social life. But the corresponding science still does not exist. Here we start it with simplest examples where there is quadratic interaction between neighboring particles and deterministic external forces. In this introduction we consider stable configurations and stable flows on one and two edge graphs. Moreover, distribution of mean (as in virial theorem) kinetic and potential energies along the graph is considered.