Related papers: The Buckley-Osthus model and the block preferentia…

Preferential attachment --- by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree --- has become the standard growth model for scale-free networks, where the asymptotic probability of a node…

With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…

We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…

In this paper we introduce a new type of preferential attachment network, the growth of which is based on the eigenvalue centrality. In this network, the agents attach most probably to the nodes with larger eigenvalue centrality which…

With ever-increasing available data, predicting individuals' preferences and helping them locate the most relevant information has become a pressing need. Understanding and predicting preferences is also important from a fundamental point…

We consider a dynamic version of the stochastic block model, in which the nodes are partitioned into latent classes and the connection between two nodes is drawn from a Bernoulli distribution depending on the classes of these two nodes. The…

There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate…

We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there…

We generalize the scale-free network model of Barab\`asi and Albert [Science 286, 509 (1999)] by proposing a class of stochastic models for scale-free interdependent networks in which interdependent nodes are not randomly connected but…

This paper proposes a stochastic block model with dynamics where the population grows using preferential attachment. Nodes with higher weighted degree are more likely to recruit new nodes, and nodes always recruit nodes from their own…

We use the framework of multivariate regular variation to analyse the extremal behaviour of preferential attachment models. To this end, we follow a directed linear preferential attachment model for a random, heavy-tailed number of steps in…

We analyze the growth models for complex networks including preferential attachment (A.-L. Barabasi and R. Albert, Science 286, 509 (1999)) and fitness model (Caldarelli et al., Phys. Rev. Lett. 89, 258702 (2002)) and demonstrate that,…

We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…

Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or…

In this paper, we study some important statistics of the random graph in the Buckley-Osthus model. This model is a modification of the well-known Bollob\'as-Riordan model. We denote the number of nodes by t, the so-called initial…

The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…