Related papers: Competing types in preferential attachment graphs …

The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied…

Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…

We study the preferential attachment model $G_n^h$. A graph $G_n^h$ is generated from a finite initial graph by adding new vertices one at a time. Each new vertex connects to $h\ge 1$ already existing vertices, and these are chosen with…

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism…

Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…

Consider the following asynchronous, opportunistic communication model over a graph $G$: in each round, one edge is activated uniformly and independently at random and (only) its two endpoints can exchange messages and perform local…

We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and…

We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…

We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We…

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…

Characterizing the structure of cities constitutes an important task since the identification of similar cities can promote sharing of respective experiences. In the present work, we consider 20 European cities from 5 respective countries…

We introduce a model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex has an associated uniform random variable which we call its location. Our model…

We focus on the majority model in a topology consisting of two coupled fully-connected networks, thereby mimicking the existence of communities in social networks. We show that a transition takes place at a value of the inter-connectivity…

We introduce a model of evolving preferential attachment trees where vertices are assigned weights, and the evolution of a vertex depends not only on its own weight, but also on the weights of its neighbours. We study the distribution of…

In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…

In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…

Trait variation and similarity among coexisting species can provide a window into the mechanisms that maintain their coexistence. Recent theoretical explorations suggest that competitive interactions will lead to groups, or clusters, of…

We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…

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…