Related papers: Preferential attachment alone is not sufficient to…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…
Preferential attachment models have been widely studied in complex networks, because they can explain the formation of many networks like social networks, citation networks, power grids, and biological networks, to name a few. Motivated by…
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…
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks.…
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…
We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution…
We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices…
We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
We study the mean length $\ell(k)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law…
Very often, when studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree-degree correlations are not present. However, simple constraints, such as the absence of multiple edges and…
Preferential attachment in a directed scale-free graph is widely used to model the evolution of social networks. Statistical analyses of social networks often relies on node based data rather than conventional repeated sampling. For our…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…