Related papers: General model for Apollonian networks
Recently, a framework for analyzing time series by constructing an associated complex network has attracted significant research interest. One of the advantages of the complex network method for studying time series is that complex network…
First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…
We investigate the differences between scale-free recursive nets constructed by a synchronous, deterministic updating rule (e.g., Apollonian nets), versus an asynchronous, random sequential updating rule (e.g., random Apollonian nets). We…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
In complex systems, responses to small perturbations are too diverse to predict how much they would be definitely, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks,…
We introduce a network growth model based on complete redirection: a new node randomly selects an existing target node, but attaches to a random neighbor of this target. For undirected networks, this simple growth rule generates unusual,…
We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…
To measure the IPv6 internet AS-level topology, a network topology discovery system, called Dolphin, was developed. By comparing the measurement result of Dolphin with that of CAIDA's Scamper, it was found that the IPv6 Internet at AS…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…
In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…
We present a simple mechanism for generating undirected scale-free networks using random walkers, where the network growth is determined by choosing parent vertices by sequential random walks. We show that this mechanism produces scale-free…
We propose a general model of unweighted and undirected networks having the scale-free property and fractal nature. Unlike the existing models of fractal scale-free networks (FSFNs), the present model can systematically and widely change…
Various real systems simultaneously exhibit scale-free and hierarchical structure. In this paper, we study analytically average distance in a deterministic scale-free network with hierarchical organization. Using a recursive method based on…
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
Here, we propose a class of scale-free networks $G(t;m)$ with some intriguing properties, which can not be simultaneously held by all the theoretical models with power-law degree distribution in the existing literature, including (i)…