Related papers: Scaling of internode distances in weighted complex…
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 describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
In heterogeneous network systems such as ecological and social networks, structural stability depends on how connectivity changes under node removal, as different removal sequences can trigger distinct modes of systemic collapse. While…
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the…
Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Scaling phenomena have been intensively studied during the past decade in the context of complex networks. As part of these works, recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks. In…
We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…
By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes,…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a…
Scale free dynamics are observed in a variety of physical and biological systems. These include neural activity in which evidence for scale freeness has been reported using a range of imaging modalities. Here, we derive the ways in which…
Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and…
Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…
We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…