Complex networks are key to describing the connected nature of the society that we live in.
This book, the second of two volumes, describes the local structure of random graph models …

Many real-world networks display a community structure. We study two random graph
models that create a network with similar community structure as a given network. One …

These lecture notes are intended to be used for master courses, where the students have a
limited prior knowledge of special topics in probability. Therefore, we have included many of …

This book focuses on percolation on high-dimensional lattices. We give a general
introduction to percolation, stating the main results and defining the central objects. We …

We formulate and study a model for inhomogeneous long-range percolation on Zd. Each
vertex x∈ Zd is assigned a non-negative weight Wx, where (Wx) x∈ Zd are iid random …

We find scaling limits for the sizes of the largest components at criticality for rank-1
inhomogeneous random graphs with power-law degrees with power-law exponent τ. We …

We investigate the component sizes of the critical configuration model, as well as the related
problem of critical percolation on a supercritical configuration model. We show that, at …

One major open conjecture in the area of critical random graphs, formulated by statistical
physicists, and supported by a large amount of numerical evidence over the last decade …

It is a fundamental question in disease modeling how the initial seeding of an epidemic,
spreading over a network, determines its final outcome. One important goal has been to find …

Consider a critical random multigraph G_n with n vertices constructed by the configuration
model such that its vertex degrees are independent random variables with the same …