Related papers: Hierarchical deposition and scale-free networks: a…

Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…

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…

Differently from theoretical scale-free networks, most of real networks present multi-scale behavior with nodes structured in different types of functional groups and communities. While the majority of approaches for classification of nodes…

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the…

We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

We propose a maximally disassortative (MD) network model which realizes a maximally negative degree-degree correlation, and study its percolation transition to discuss the effect of a strong degree-degree correlation on the percolation…

Conventional scaling of neural networks typically involves designing a base network and growing different dimensions like width, depth, etc. of the same by some predefined scaling factors. We introduce an automated scaling approach…

Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive…

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…

A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on 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 have analysed some structural properties of scale-free networks with the same degree distribution. Departing from a degree distribution obtained from the Barab\'asi-Albert (BA) algorithm, networks were generated using four additional…

The clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph. In real networks it decreases with the vertex degree, which has been taken as a signature of the network hierarchical structure. Here we show…

It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated…

There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…

Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the…

We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units…

Clustering is typically measured by the ratio of triangles to all triples, open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks…

We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and…