Percolation is the simplest fundamental model in statistical mechanics that exhibits phase
transitions signaled by the emergence of a giant connected component. Despite its very …

The world is becoming a more conjunct place and the number of data sources such as
social networks, online transactions, web search engines, and mobile devices is increasing …

Over the past decade, the use of networks has led to a new modelling paradigm combining
several branches of science, including physics, mathematics, biology and social sciences …

From social networks such as Facebook, the World Wide Web and the Internet, to the
complex interactions between proteins in the cells of our bodies, we constantly face the …

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions
in real-world networks. We first provide a rigorous definition of power-law distributions …

How to understand the propagation properties of infectious diseases among the population
is an important topic in the field of epidemic modelling. In this paper, we investigate the …

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 …

The “classical” random graph models, in particular G (n, p), are “homogeneous,” in the
sense that the degrees (for example) tend to be concentrated around a typical value. Many …

Statistical network modelling has focused on representing the graph as a discrete structure,
namely the adjacency matrix. When assuming exchangeability of this array—which can aid …

Random graphs with given degrees are a natural next step in complexity beyond the Erdős–
Rényi model, yet the degree constraint greatly complicates simulation and estimation. We …