Related papers: Generic scale of the "scale-free" growing networks

Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…

We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units…

We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on…

In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…

We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…

A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…

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…

A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…

Complex networks across various fields are often considered to be scale free -- a statistical property usually solely characterized by a power-law distribution of the nodes' degree $k$. However, this characterization is incomplete. In…

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…

We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…

Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…

We introduce a simple one-parameter network growth algorithm which is able to reproduce a wide variety of realistic network structures but without having to invoke any global information about node degrees such as preferential-attachment…

Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the…

We analyze the degree distribution's cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices $N$ is ruled by the topological constraints induced by the connectivity structure of the network.…

We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…

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,…