Related papers: Pair Correlations in Scale-Free Networks
We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent…
We study synchronization phenomena in scale-free networks of asymetrically coupled dynamical systems featuring degree-degree correlation in the connection wiring. We show that when the interaction is dominant from the high-degree to the…
The degree-degree correlation is important in understanding the structural organization of a network and the dynamics upon a network. Such correlation is usually measured by the assortativity coefficient $r$, with natural bounds $r \in…
The paper orders certain important issues related to both uncorrelated and correlated networks with hidden variables. In particular, we show that networks being uncorrelated at the hidden level are also lacking in correlations between node…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…
Collaboration networks are studied as an example of growing bipartite networks. These have been previously observed to have structure such as positive correlations between nearest-neighbour degrees. However, a detailed understanding of the…
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…
Based on the concept and techniques of first-passage probability in Markov chain theory, this letter provides a rigorous proof for the existence of the steady-state degree distribution of the scale-free network generated by the…
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…
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,…
The sampling of scale-free networks in Molecular Biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms…
We investigate the role of degree correlation among nodes on the stability of complex networks, by studying spectral properties of randomly weighted matrices constructed from directed Erd\"{o}s-R\'enyi and scale-free random graph models. We…
Many naturally occurring networks have a power-law degree distribution as well as a non-zero degree correlation. Despite this, most studies analyzing the robustness to random node-deletion and vulnerability to targeted node-deletion have…
In this paper we study a model of synchronization process on scale free networks with degree-degree correlations. This model was already studied on this kind of networks without correlations by Pastore y Piontti {\it et al.}, Phys. Rev. E…
Degree ssortativity is the tendency for nodes of high degree (resp.low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is sually quantified by the Pearson correlation coefficient of the degree-degree…
Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A…
Networks with a scale-free degree distribution are widely thought to promote cooperation in various games. Herein, by studying the well-known prisoner's dilemma game, we demonstrate that this need not necessarily be true. For the very same…
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,…
Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms…