Related papers: Assortativity in networks
We examine two properties of complex networks, the robustness against targeted node removal (attack) and the transport efficiency in terms of degree correlation in node connection by numerical evaluation of exact analytic expressions. We…
A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…
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…
Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by…
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…
In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist,…
The Japanese shareholding network at the end of March 2002 is studied. To understand the characteristics of this network intuitively, we visualize it as a directed graph and an adjacency matrix. Especially detailed features of networks…
Nominal assortativity (or discrete assortativity) is widely used to characterize group mixing patterns and homophily in networks, enabling researchers to analyze how groups interact with one another. Here we demonstrate that the measure…
We study the effects of the degree-degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for…
Self-similar networks with scale-free degree distribution have recently attracted much attention, since these apparently incompatible properties were reconciled in a paper by Song et al. by an appropriate box-counting method that enters the…
In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free…
We define a statistical ensemble of non-degenerate graphs, i.e. graphs without multiple- and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier…
In the new field of financial systemic risk, the network of interbank counterparty relationships can be described as a directed random graph. In "cascade models" of systemic risk, this "skeleton" acts as the medium through which financial…
Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…
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…
We connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy coming from the vertex shift, which is related to the spectral radius of the graph's adjacency matrix, the…
We generate correlated scale-free networks in the configuration model through a new rewiring algorithm which allows to tune the Newman assortativity coefficient $r$ and the average degree of the nearest neighbors $K$ (in the range $-1\le r…
Graph alignment - identifying node correspondences between two graphs - is a fundamental problem with applications in network analysis, biology, and privacy research. While substantial progress has been made in aligning correlated…
This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is…
Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…