Related papers: Modern architecture of random graphs: Construction…

(a) We propose a ``static'' construction procedure for random networks with given correlations of the degrees of the nearest-neighbor vertices. This is an equilibrium graph, maximally random under the constraint that its degree-degree…

We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…

Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…

In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on…

A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…

1. The birth of network science. 2. What are random networks? 3. Adjacency matrix. 4. Degree distribution. 5. What are simple networks? Classical random graphs. 6. Birth of the giant component. 7. Topology of the Web. 8.Uncorrelated…

Uncorrelated random scale-free networks are useful null models to check the accuracy an the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable to generate random uncorrelated…

We define a statistical ensemble of non-degenerate graphs, i.e. graphs without multiple- and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier…

In statistical physics any given system can be either at an equilibrium or away from it. Networks are not an exception. Most network models can be classified as either equilibrium or growing. Here we show that under certain conditions there…

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…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…

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…

We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…

We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…

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…

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…

Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical…

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…

A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be…

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…