Finding structures in large-scale graphs

One of the most vexing challenges of working with graphical structures is that most algorithms scale poorly as the graph becomes very large. The computation is extremely expensive even for polynomial algorithms, thus making it desirable to devise fast approximation algorithms. We herein propose a framework using advanced tools 1-6 from random graph theory and spectral graph theory to address the quantitative analysis of the structure and dynamics of large-scale networks. This framework enables one to carry out analytic computations of observable network structures and capture the most relevant and refined quantities of realworld networks.