Random Graphs Geometry and Asymptotic Structure

The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However due to their diverse nature the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover the theory itself even in its most basic forms is often considered too advanced to be part of undergraduate curricula and those who are interested usually learn it mostly through self-study covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.