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 …

Real-world networks, like social networks or the internet infrastructure, have structural
properties such as large clustering coefficients that can best be described in terms of an …

We analyze the popular push-pull protocol for spreading a rumor in networks. Initially, a
single node knows of a rumor. In each succeeding round, every node chooses a random …

We investigate a class of growing graphs embedded into the d-dimensional torus where
new vertices arrive according to a Poisson process in time, are randomly placed in space …

PageRank is a well-known algorithm for measuring centrality in networks. It was originally
proposed by Google for ranking pages in the World Wide Web. One of the intriguing …

In Chung-Lu random graphs, a classic model for real-world networks, each vertex is
equipped with a weight drawn from a power-law distribution, and two vertices form an edge …

We study preferential attachment models where vertices enter the network with iid random
numbers of edges that we call the out-degree. We identify the local limit of such models …

We study geometric random graphs defined on the points of a Poisson process in d-
dimensional space, which additionally carry independent random marks. Edges are …

We study typical distances in a geometric random graph on the hyperbolic plane. Introduced
by Krioukov et al.~\cite {ar: Krioukov} as a model for complex networks, $ N $ vertices are …