Related papers: Apollonian networks
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…
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…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
We propose the n-clique network as a powerful tool for understanding global structures of combined highly-interconnected subgraphs, and provide theoretical predictions for statistical properties of the n-clique networks embedded in a…
A family of graphs optimized as the topologies for supercomputer interconnection networks is proposed. The special needs of such network topologies, minimal diameter and mean path length, are met by special constructions of the weight…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
Networks with long-range connections obeying a distance-dependent power law of sufficiently small exponent display superdiffusion, L\'evy flights and robustness properties very different from the scale-free networks. It has been proposed…
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…
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 $\mathcal{T}_{t}$,…
A remarkable feature of static granular matter is the distribution of force along intricate networks. Even regular inter-particle contact networks produce wildly inhomogeneous force networks where certain "chains" of particles carry forces…
A set of general allometric scaling laws is derived for different systems represented by tree networks. The formulation postulates self-similar networks with an arbitrary number of branches developed in each generation, and with an…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…
In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
Small world models are networks consisting of many local links and fewer long range 'shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution…
Complex networks possess a rich, multi-scale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one…
Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…