Related papers: Degree-degree correlations in random graphs with h…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…
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 investigate degree correlations in two online social networks where users are connected through different types of links. We find that, while subnetworks in which links have a positive connotation, such as endorsement and trust, are…
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 general relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks.…
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…
Networks facilitate the spread of cascades, allowing a local perturbation to percolate via interactions between nodes and their neighbors. We investigate how network structure affects the dynamics of a spreading cascade. By accounting for…
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…
An important problem in modeling networks is how to generate a randomly sampled graph with given degrees. A popular model is the configuration model, a network with assigned degrees and random connections. The erased configuration model is…
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,…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
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…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
This paper proposes a new class of assortativity measures for weighted and directed networks. We extend the classical Newman's degree-degree assortativity by considering nodes' attributes different from the degree. Moreover, we propose…
We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129-132]. For…