Related papers: Networks with given two-point correlations: hidden…
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…
We discuss a simple method of constructing correlated random networks, which was recently proposed by M. Bogu~n'a and R. Pastor-Satorras (cond-mat/0306072). The result of this construction procedure is a sparse network whose degree--degree…
Dynamical processes on complex networks such as information propagation, innovation diffusion, cascading failures or epidemic spreading are highly affected by their underlying topologies as characterized by, for instance, degree-degree…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections.…
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…
Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated, i.e. disassortative? With a view to answering this long-standing question, we define a general class of degree-degree…
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the…
Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant…
We introduce an exponential random graph model for networks with a fixed degree distribution and with a tunable degree-degree correlation. We then investigate the nature of a percolation transition in the correlated network with the Poisson…
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…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other…
While degree correlations are known to play a crucial role for spreading phenomena in networks, their impact on the propagation speed has hardly been understood. Here we investigate a tunable spreading model on scale-free networks and show…
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…
The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
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…
We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully…
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,…