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 …

In the past decade, geometric network models have received vast attention in the literature.
These models formalize the natural idea that similar vertices are likely to connect. Because …

Turing patterns, arising from the interplay between competing species of diffusive particles,
have long been an important concept for describing nonequilibrium self-organization in …

One of the pillars of the geometric approach to networks has been the development of model-
based mapping tools that embed real networks in its latent geometry. In particular, the tool …

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 …

Motivated by problems of hyperbolic stochastic geometry we introduce and study the class of
beta-star polytopes. A beta-star polytope is defined as the convex hull of an inhomogeneous …

Poisson processes in the space of k-dimensional totally geodesic subspaces (k-flats) in a d-
dimensional standard space of constant curvature κ∈{− 1, 0, 1} are studied, whose …

We consider a large class of spatially-embedded random graphs that includes among others
long-range percolation, continuum scale-free percolation and the age-dependent random …

Modularity is a quantity which has been introduced in the context of complex networks in
order to quantify how close a network is to an ideal modular network in which the nodes form …

A recent trend in the context of graph theory is to bring theoretical analyses closer to
empirical observations by focusing the studies on random graph models that are used to …