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 …

We perform an empirical study of the preferential attachment phenomenon in temporal
networks and show that on the Web, networks follow a nonlinear preferential attachment …

We define a class of growing networks in which new nodes are given a spatial position and
are connected to existing nodes with a probability mechanism favoring short distances and …

Many statistical models for networks overlook the fact that most real-world networks are
formed through a growth process. To address this, we introduce the Preferential Attachment …

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 …

We study a dynamical random network model in which at every construction step a new
vertex is introduced and attached to every existing vertex independently with a probability …

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 a general preferential attachment and Pólya's urn model. At each step a new
vertex is introduced, which can be connected to at most one existing vertex. If it is …

We consider models of evolving networks G n: n≥ 0 modulated by two parameters: an
attachment function f: N 0→ R+ and a (possibly random) attachment sequence mi: i≥ 1 …