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Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and…
The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidden of self-connection and…
We propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple weight-driven dynamics and generates networks exhibiting…
Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
In this work we study a simple evolutionary model of bipartite networks which its evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary…
Network theory provides a rich toolbox consisting of methods, measures, and models for studying the structure and dynamics of complex systems found in nature, society, or technology. Recently, it has been pointed out that many real-world…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
Most real-world networks display not only a heterogeneous distribution of degrees, but also a heterogeneous distribution of weights in the strengths of the connections. Each of these heterogeneities alone has been shown to suppress…
We investigate the degree-degree correlations in the Erdos-Renyi networks, the growing exponential networks and the scale-free networks. We demonstrate that these correlations are the largest for the exponential networks. We calculate also…
A key measure that has been used extensively in analyzing complex networks is the degree of a node (the number of the node's neighbors). Because of its discrete nature, when the degree measure was used in analyzing weighted networks,…
Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
In their recent work "Scale-free networks are rare", Broido and Clauset address the problem of the analysis of degree distributions in networks to classify them as scale-free at different strengths of "scale-freeness." Over the last two…
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces.…
The spread of perturbative signals in complex networks is governed by the combined effect of the network topology and its intrinsic nonlinear dynamics. Recently, the resulting spreading patterns have been analyzed and predicted, shown to…
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…
Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…
Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks.…