Related papers: Deterministic hierarchical networks
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
The importance of classifying connections in large graphs has been the motivation for a rich line of work on distributed subgraph finding that has led to exciting recent breakthroughs. A crucial aspect that remained open was whether…
Many real-world complex networks simultaneously exhibit topological features of scale-free behaviour and hierarchical organization. In this regard, deterministic scale-free [A.-L. Barab\'asi \etal, Physica A, 299, 3 (2001)] and…
In this paper we introduce a family of planar, modular and self-similar graphs which have small-world and scale-free properties. The main parameters of this family are comparable to those of networks associated to complex systems, and…
A degree-corrected distribution-free model is proposed for weighted social networks with latent structural information. The model extends the previous distribution-free models by considering variation in node degree to fit real-world…
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…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
Discoveries of the scale-free and small-world features are reported on a network constructed from the seismic data. It is shown that the connectivity distribution decays as a power law, and the value of the degrees of separation, i.e., the…
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…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Many biological networks have been labelled scale-free as their degree distribution can be approximately described by a powerlaw distribution. While the degree distribution does not summarize all aspects of a network it has often been…
Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
Stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks. Most blockmodels, however, ignore variation in vertex degree, making them…
We consider deterministic distributed communication in wireless ad hoc networks of identical weak devices under the SINR model without predefined infrastructure. Most algorithmic results in this model rely on various additional features or…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free…