Related papers: Nonparametric estimation of the preferential attac…

We study the following preferential attachment variant of the classical Erdos-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly…

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…

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…

In order to better understand dynamical functions on amounts of natural and man-made complex systems, lots of researchers from a wide range of disciplines, covering statistic physics, mathematics, theoretical computer science, and so on,…

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…

Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…

In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…

Reciprocity characterizes the information exchange between users in a network, and some empirical studies have revealed that social networks have a high proportion of reciprocal edges. Classical directed preferential attachment (PA) models,…

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…

Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs…

Few-shot models have become a popular topic of research in the past years. They offer the possibility to determine class belongings for unseen examples using just a handful of examples for each class. Such models are trained on a wide range…

One-shot image classification aims to train image classifiers over the dataset with only one image per category. It is challenging for modern deep neural networks that typically require hundreds or thousands of images per class. In this…

Preferential attachment, homophily and, their consequences such as the glass ceiling effect have been well-studied in the context of undirected networks. However, the lack of an intuitive, theoretically tractable model of a directed,…

Effective image classification hinges on discerning relevant features from both foreground and background elements, with the foreground typically holding the critical information. While humans adeptly classify images with limited exposure,…

Simple growth mechanisms have been proposed to explain the emergence of seemingly universal network structures. The widely-studied model of preferential attachment assumes that new nodes are more likely to connect to highly connected nodes.…

We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…

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…

We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the…

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…

Identifying power-law scaling in real networks - indicative of preferential attachment - has proved controversial. Critics argue that measuring the temporal evolution of a network directly is better than measuring the degree distribution…