Related papers: Fractality and degree correlations in scale-free n…
We propose a mapping from fracture systems consisting of intersecting fracture sheets in three dimensions to an abstract network consisting of nodes and links. This makes it possible to analyze fracture systems with the methods developed…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
The degree-degree correlation is crucial in understanding the structural properties of and dynamics occurring upon network, and is often measured by the assortativity coefficient $r$. In this paper, we first study this measure in detail and…
We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this…
Many social networks exhibit assortative mixing so that the predictions of uncorrelated models might be inadequate. To analyze the role of assortativity we introduce an algorithm which changes correlations in a network and produces…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
We study the synchronizability and the synchronization dynamics of networks of nonlinear oscillators. We investigate how the synchronization of the network is influenced by some of its topological features such as variations of the power…
The conventional wisdom is that social networks exhibit an assortative mixing pattern, whereas biological and technological networks show a disassortative mixing pattern. However, the recent research on the online social networks modifies…
The fluctuation of dynamic variables in complex networks is known to depend on the dimension and the heterogeneity of the substrate networks. Previous studies, however, have reported inconsistent results for the scaling behavior of…
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…
There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized,…
The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…
We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…
Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal $\Lambda $. With rigorous mathematical results we…
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.…
Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been…