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 …

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 …

The style of mathematical models known to probabilists as Interacting Particle Systems and
exemplified by the Voter, Exclusion and Contact processes have found use in many …

In this paper we study weighted distances in scale-free spatial network models: hyperbolic
random graphs, geometric inhomogeneous random graphs and scale-free percolation. In …

In this paper we explore first passage percolation (FPP) on the Erdős–Rényi random graph
Gn (pn), where we assign independent random weights, having an exponential distribution …

We consider first passage percolation on the configuration model with n vertices, and
general independent and identically distributed edge weights assumed to have a density …

In this book, we discuss stochastic processes on random graphs. The understanding of such
processes is interesting from an applied perspective, since random graphs serve as models …

We study a ferromagnetic Ising model on random graphs with a power-law degree
distribution and compute the thermodynamic limit of the pressure when the mean degree is …

We provide a complete description of the giant component of the Erdős‐Rényi random
graph article mathrsfs amsmath empty (n, p) as soon as it emerges from the scaling window …

The metric backbone of a weighted graph is the union of all-pairs shortest paths. It is
obtained by removing all edges $(u, v) $ that are not the shortest path between $ u $ and $ v …