" 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 …

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 …

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 …

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 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 …

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

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 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 …