Networks are finite metric spaces, with distances defined by the shortest paths between
nodes. However, this is not the only form of network geometry: two others are the geometry …

Random graph (RG) models play a central role in complex networks analysis. They help us
to understand, control, and predict phenomena occurring, for instance, in social networks …

" This rigorous introduction to network science presents random graphs as models for real-
world networks. Such networks have distinctive empirical properties and a wealth of new …

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 …

Analyzing massive complex networks yields promising insights about our everyday lives.
Building scalable algorithms to do so is a challenging task that requires a careful analysis …

Hyperbolic geometry appears to be intrinsic in many large real networks. We construct and
implement a new maximum likelihood estimation algorithm that embeds scale-free graphs in …

Large real-world networks are typically scale-free. Recent research has shown that such
graphs are described best in a geometric space. More precisely, the Internet can be mapped …

We investigate random graphs on the points of a Poisson process in d-dimensional space,
which combine scale-free degree distributions and long-range effects. Every Poisson point …

Clustering–the tendency for neighbors of nodes to be connected–quantifies the coupling of
a complex network to its latent metric space. In random geometric graphs, clustering …