Related papers: Multi-directed Eulerian growing networks
We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
We study the problem of explaining a rich class of behavioral properties of deep neural networks. Distinctively, our influence-directed explanations approach this problem by peering inside the network to identify neurons with high influence…
For $\Delta$ a finite connected nontrivial directed multigraph, we prove: 1. $\Delta$ has a directed circuit using each directed edge exactly once if and only if both each pair of distinct vertices of $\Delta$ occur in a common directed…
Funnelling effect, in the context of searching on networks, precisely indicates that the search takes place through a few specific nodes. We define the funnelling capacity $f$ of a node as the fraction of successful dynamic paths through it…
Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
It has been discovered recently that many social, biological and ecological systems have the so-called small-world and scale-free features, which has provoked new research interest in the studies of various complex networks. Yet, most…
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…
We introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact…
The population structure often impacts evolutionary dynamics. In constant-selection evolutionary dynamics between two types, amplifiers of selection are networks that promote the fitter mutant to take over the entire population, and…
Many complex systems may be described not by one, but by a number of complex networks mapped one on the other in a multilayer structure. The interactions and dependencies between these layers cause that what is true for a distinct single…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although…
Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…
A new network evolution model is introduced in this paper. The model is based on co-operations of $N$ units. The units are the nodes of the network and the co-operations are indicated by directed links. At each evolution step $N$ units…
We show that the protein-protein interaction networks can be surprisingly well described by a very simple evolution model of duplication and divergence. The model exhibits a remarkably rich behavior depending on a single parameter, the…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic…
Estimating dependence relationships between variables is a crucial issue in many applied domains, such as medicine, social sciences and psychology. When several variables are entertained, these can be organized into a network which encodes…