Related papers: Skeleton and fractal scaling in complex networks
Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal $\Lambda $. With rigorous mathematical results we…
We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models…
In this paper, a simple dynamical model in which fractal networks are formed by self-organized critical (SOC) dynamics is proposed; the proposed model consists of growth and collapse processes. It has been shown that SOC dynamics are…
Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
Spanning trees are an important quantity characterizing the reliability of a network, however, explicitly determining the number of spanning trees in networks is a theoretical challenge. In this paper, we study the number of spanning trees…
In heterogeneous network systems such as ecological and social networks, structural stability depends on how connectivity changes under node removal, as different removal sequences can trigger distinct modes of systemic collapse. While…
It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We…
With an increasing emphasis on network security, much more attention has been attracted to the vulnerability of complex networks. The multi-scale evaluation of vulnerability is widely used since it makes use of combined powers of the links'…
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
The fractal structure with a power index of 2 is considered within the framework of the universe with the linear law of evolution. The fractal structure arises due to the linear evolution of the scale of mass. Potential fluctuations connect…
It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in…