Related papers: Preferential attachment hypergraph with vertex dea…

Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…

Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to…

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 high degrees. The competition of preferential attachment and…

Subgraphs are very important for understanding structure and function of complex networks. Dyad and triad are the elementary subgraphs. We focus on the distribution of their act degree defined as the number of activities, events or…

It has been discovered recently that many social, biological and ecological systems have the so-called small-world and scale-free features, which has provoked new research interest in the studies of various complex networks. Yet, most…

The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…

We consider the preferential attachment model with location-based choice introduced by Haslegrave, Jordan and Yarrow as a model in which condensation phenomena can occur [Haslegrave et al. 2020]. In this model every vertex carries an…

Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…

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…

We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…

Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps.…

Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…

Mutualism is a biological interaction mutually beneficial for both species involved, such as the interaction between plants and their pollinators. Real mutualistic communities can be understood as weighted bipartite networks and they…

Real-world networks are generally claimed to be scale-free, meaning that the degree distributions follow the classical power-law, at least asymptotically. Yet, closer observation shows that the classical power-law distribution is often…

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

Preferential attachment models were shown to be very effective in predicting such important properties of real-world networks as the power-law degree distribution, small diameter, etc. Many different models are based on the idea of…

In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…

In this paper, we proposed an evolving model via the hypergraph to illustrate the evolution of the citation network. In the evolving model, we consider the mechanism combined with preferential attachment and the aging influence. Simulation…