Related papers: Dense Power-law Networks and Simplicial Complexes
We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already…
Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks $\mathcal{T}_{t}$,…
Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…
We study the organization and dynamics of growing directed networks. These networks are built by adding nodes successively in such a way that each new node has $K$ directed links to the existing ones. The organization of a growing directed…
It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
In recent years, there has been a growing recognition that higher-order structures are important features in real-world networks. A particular class of structures that has gained prominence is known as a simplicial complex. Despite their…
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…
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…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
In this letter, we proposed an ungrowing scale-free network model, wherein the total number of nodes is fixed and the evolution of network structure is driven by a rewiring process only. In spite of the idiographic form of $G$, by using a…
In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…