Related papers: Assortative mixing by degree makes a network more …
Heterogeneity is a key aspect of complex networks, often emerging by looking at the distribution of node properties, from the milestone observations on the degree to the recent developments in mixing pattern estimation. Mixing patterns, in…
A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…
We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are…
Directed networks are ubiquitous and are necessary to represent complex systems with asymmetric interactions---from food webs to the World Wide Web. Despite the importance of edge direction for detecting local and community structure, it…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
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…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…
Assortativity was first introduced by Newman and has been extensively studied and applied to many real world networked systems since then. Assortativity is a graph metrics and describes the tendency of high degree nodes to be directly…
Recent advances have focused mainly on the resilience of the monoplex network in attacks targeting random nodes or links, as well as the robustness of the network against cascading attacks. However, very little research has been done to…
Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for…
Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA, 108, 3838 (2011)], using simulations, that scale-free networks with "onion structure" are very robust against targeted high degree attacks. The onion structure is a…
Network science have constantly been in the focus of research for the last decade, with considerable advances in the controllability of their structural. However, much less effort has been devoted to study that how to improve the…
To characterize the dynamical features of seismicity as a complex phenomenon, the seismic data is mapped to a growing random graph, which is a small-world scale-free network. Here, hierarchical and mixing properties of such a network are…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
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…
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…
For any initial correlated network after any kind of attack where either nodes or edges are removed, we obtain general expressions for the degree-degree probability matrix and degree distribution. We show that the proposed analytical…