Related papers: Assortativity in networks
We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp {[}-\beta \H(\c)…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
We introduce the concept of Random Sequential Renormalization (RSR) for arbitrary networks. RSR is a graph renormalization procedure that locally aggregates nodes to produce a coarse grained network. It is analogous to the (quasi-)parallel…
Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…
Inhomogeneity in networks can be detected by the analysis of the correlation of the total degree of nearest neighbors. This is illustrated by two models. The first one is a random multi-partitions network that the Aboav Weaire law, which…
The reliability of a network is an important parameter to consider when building a network. Different characteristics of the network can become unreliable over time or from other outside forces. In a simple setting, we model a network as a…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
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…
Core-periphery is a key feature of large-scale networks underlying a wide range of social, biological, and transportation phenomena. Despite its prevalence in empirical data, it is unclear whether this property is a consequence of more…
In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the…
In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], Schneider et al. proposed a new measure for network robustness and investigated optimal networks with respect to this quantity. For networks with a power-law degree…
Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…
The function or performance of a network is strongly dependent on its robustness, quantifying the ability of the network to continue functioning under perturbations. While a wide variety of robustness metrics have been proposed, they have…
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…
Many applications produce massive complex networks whose analysis would benefit from parallel processing. Parallel algorithms, in turn, often require a suitable network partition. For solving optimization tasks such as graph partitioning on…
By constructing a multicanonical Monte Carlo simulation, we obtain the full probability distribution $\rho_N(r)$ of the degree assortativity coefficient $r$ on configuration networks of size $N$ by using the multiple histogram reweighting…
Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes 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…
Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the base tree, by adding additional…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…