Related papers: Random Apollonian Networks

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…

In this paper, a simply rule that generates scale-free networks with very large clustering coefficient and very small average distance is presented. These networks are called {\bf Multistage Random Growing Networks}(MRGN) as the adding…

We present and study in this paper a simple algorithm that produces so called growing Parallel Random Apollonian Networks (P-RAN) in any dimension d. Analytical derivations show that these networks still exhibit small-word and scale-free…

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…

In this paper, by both simulations and theoretical predictions we study two and three node (or degree) correlations in random Apollonian network (RAN), which have small-world and scale-free topologies. Using the rate equation approach under…

We propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called simplex triangulation networks(STNs) as they can be considered as a kind of…

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 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…

This paper studies Random and Evolving Apollonian networks (RANs and EANs), in d dimension for any d>=2, i.e. dynamically evolving random d dimensional simplices looked as graphs inside an initial d-dimensional simplex. We determine 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…

In this paper, we study the distribution of distances in random Apollonian network structures (RANS), a family of graphs which has a one-to-one correspondence with planar ternary trees. Using multivariate generating functions that express…

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…

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 carry out comparative studies of random walks on deterministic Apollonian networks (DANs) and random Apollonian networks (RANs). We perform computer simulations for the mean first passage time, the average return time, the mean-square…

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…

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…

Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…

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…

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…

We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the…