Related papers: Assortativity in networks
Motivated by a recently introduced network growth mechanism that rely on the ranking of node prestige measures [S. Fortunato \emph{et al}., Phys. Rev. Lett. \textbf{96}, 218701 (2006)], a rank-based model for weighted network evolution is…
Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive…
By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree…
Assortativity coefficients are important metrics to analyze both directed and undirected networks. In general, it is not guaranteed that the fitted model will always agree with the assortativity coefficients in the given network, and the…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to…
It has been observed that real-world social networks often exhibit stratification along economic or other lines, with consequences for class mobility and access to opportunities. With the rise in human interaction data and extensive use of…
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…
In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree…
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 $r$,…
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…
We study the synchronizability and the synchronization dynamics of networks of nonlinear oscillators. We investigate how the synchronization of the network is influenced by some of its topological features such as variations of the power…
Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
We investigate the impact of degree-degree correlations on the spectra of networks. Even though density distributions exhibit drastic changes depending on the (dis)assortative mixing and the network architecture, the short range…
The sorting number of a graph with $n$ vertices is the minimum depth of a sorting network with $n$ inputs and outputs that uses only the edges of the graph to perform comparisons. Many known results on sorting networks can be stated in…
We introduce, and analyze, three measures for degree-degree dependencies, also called degree assortativity, in directed random graphs, based on Spearman's rho and Kendall's tau. We proof statistical consistency of these measures in general…
Degree correlation is a crucial measure in networks, significantly impacting network topology and dynamical behavior. The degree sequence of a network is a significant characteristic, and altering network degree correlation through…
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…