Statistical Mechanics of Complex Graphs

Abstract

Modelling of graphs as abstract mathematical structures is often utilised in myriad of studies across the whole spectrum of scientific fields. This paper aims to investigate some of the graph theory characteristics of complex systems. Such investigation is applicable for real-world phenomena studies and optimisation simulations of models representable by graph theory structures. A random model generation algorithm was developed to build random graphs that were further perturbed by adding edges according to a custom preferential edge attachment algorithm. The edge attachment algorithm forces nodes in the model to coalesce into large but fewer components. Analysis of the analytically validated model graph structures by means of node degree histograms supports the proposed behaviour of graphs upon new edge addition.