Related papers: Type-II Apollonian Model

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…

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…

Experimentally observed complex networks are often scale-free, small-world and have unexpectedly large number of small cycles. Apollonian network is one notable example of a model network respecting simultaneously having all three of these…

We introduce a family of complex networks that interpolates between the Apollonian network and its binary version, recently introduced in [Phys. Rev. E \textbf{107}, 024305 (2023)], via random removal of nodes. The dilution process allows…

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…

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…

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 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…

Although two-dimensional periodic structures have functioned as the primary platform for exploring topological phenomena, recent advances have substantially expanded this research boundary to include more intricate, aperiodic structures:…

We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and…

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…

In this paper we study the toughness of Random Apollonian Networks (RANs), a random graph model which generates planar graphs with power-law properties. We consider their important characteristics: every RAN is a uniquely representable…

We introduce a general deterministic model for Apollonian Networks in an iterative fashion. The networks have small-world effect and scale-free topology. We calculate the exact results for the degree exponent, the clustering coefficient and…

Let $r$ and $d$ be positive integers with $r<d$. Consider a random $d$-ary tree constructed as follows. Start with a single vertex, and in each time-step choose a uniformly random leaf and give it $d$ newly created offspring. Let ${\mathcal…

Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

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 two types of evolving networks: evolutionary Apollonian networks (EAN) and general deterministic Apollonian networks (GDAN), established by simple iteration algorithms. We investigate the two networks by both simulation and…

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…

In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called {\bf Random Apollonian Networks}(RAN) as they can be considered…