Related papers: Model of Simplicial Complexes with dimension-wise …
We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either…
A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the $p$-type case we derive a framework for studying the tree where a type $i$ vertex generates new type $j$ vertices…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
In this paper, we analyze assortativity of preferential attachment models. We deal with a wide class of preferential attachment models (PA-class). It was previously shown that the degree distribution in all models of the PA-class follows a…
Higher-order network analysis uses the ideas of hypergraphs, simplicial complexes, multilinear and tensor algebra, and more, to study complex systems. These are by now well established mathematical abstractions. What's new is that the ideas…
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
A network is scale-free if its connectivity density function is proportional to a power-law distribution. Scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the…
Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and…
We introduce and study a general model of social network formation and evolution based on the concept of preferential link formation between similar nodes and increased similarity between connected nodes. The model is studied numerically…
Navigability, an ability to find a logarithmically short path between elements using only local information, is one of the most fascinating properties of real-life networks. However, the exact mechanism responsible for the formation of…
Concepts in a certain domain of science are linked via intrinsic connections reflecting the structure of knowledge. To get a qualitative insight and a quantitative description of this structure, we perform empirical analysis and modeling of…
In this paper we present a generalized model for network growth that links the microscopical agent strategies with the large scale behavior. This model is intended to reproduce the largest number of features of the Internet network at the…
The co-evolution of structure and dynamics, known as adaptivity, is a fundamental property in various systems and drives diverse emergent behaviors. However, the adaptivity in previous works is primarily stemmed from pairwise situations,…
A few of evolving models in hypernetworks have been proposed based on uniform growth. In order to better depict the growth mechanism and competitive aspect of real hypernetworks, we propose a model in term of the non-uniform growth. Besides…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Social scientists have long appreciated that relationships between individuals cannot be described from observing a single domain, and that the structure across domains of interaction can have important effects on outcomes of interest…
Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have…