Related papers: Self-similar disk packings as model spatial scale-…
Spatially constrained planar networks are frequently encountered in real-life systems. In this paper, based on a space-filling disk packing we propose a minimal model for spatial maximal planar networks, which is similar to but different…
We review recent results on the topological properties of two spatial scale-free networks, the inherent structure and Apollonian networks. The similarities between these two types of network suggest an explanation for the scale-free…
We introduce a new family of networks, the Apollonian networks, that are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs. These networks have a wide range of applications ranging from the description of…
There is a well-known relationship between the binary Pascal's triangle and Sierpinski triangle in which the latter obtained from the former by successive modulo 2 additions on one of its corners. Inspired by that, we define a binary…
Evolutionary game theory is employed to study topological conditions of scale-free networks for the evolution of cooperation. We show that Apollonian Networks (ANs) are perfect scale-free networks, on which cooperation can spread to all…
We study the topology of e-mail networks with e-mail addresses as nodes and e-mails as links using data from server log files. The resulting network exhibits a scale-free link distribution and pronounced small-world behavior, as observed in…
We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the…
Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other…
We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) random scale-free topology, (ii)…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…
In this paper we find an exact analytical expression for the number of spanning trees in Apollonian networks. This parameter can be related to significant topological and dynamic properties of the networks, including percolation, epidemic…
Inversive geometry can be used to generate exactly self-similar space-filling sphere packings. We present a construction method in two dimensions and generalize it to search for packings in higher dimensions. We newly discover 29…
We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their…
The conformation space of a 20-residue antiparallel $\beta$-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Conformations are nodes of the network, and the transitions between them are links. The…
We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the…
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.…
Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Moreover, experimental studies of morphology indicate that neurons develop a network of small-world-like connections, with the…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
Considering agricultural landscapes as networks can provide information about spatial connectivity relevant for a wide range of applications including pollination, pest management, and ecology. Global agricultural networks are…
A common feature of biological networks is the geometric property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks, show self-similar…