Related papers: Rigorous results on the threshold network model

In distinction to the Neumann case the squeezing limit of a Dirichlet network leads in the threshold region generically to a quantum graph with disconnected edges, exceptions may come from threshold resonances. Our main point in this paper…

We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…

This paper studies the effect of boundary value conditions on consensus networks. Consider a network where some nodes keep their estimates constant while other nodes average their estimates with that of their neighbors. We analyze such…

In communication networks theory the concepts of networkness and network surplus have recently been defined. Together with transmission and betweenness centrality, they were based on the assumption of equal communication between vertices.…

Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

In order to conduct analyses of networked systems where connections between individuals take on a range of values - counts, continuous strengths or ordinal rankings - a common technique is to dichotomize the data according to their…

It has been argued that the observed anticorrelation between the degrees of adjacent vertices in the network representation of the Internet has its origin in the restriction that no two vertices have more than one edge connecting them. Here…

Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…

This article gives a new proof that fully connected neural networks with random weights and biases converge to Gaussian processes in the regime where the input dimension, output dimension, and depth are kept fixed, while the hidden layer…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

In a random graph model based on 3-interactions we give the joint asymptotic distribution of weights and degrees and prove scale-free property for the model. Moreover, we determine the asymptotics of the maximal weight and the maximal…

In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…

Suppose that under the action of gravity, liquid drains through the unit $d$-cube via a minimal-length network of channels constrained to pass through random sites and to flow with nonnegative component in one of the canonical orthogonal…

In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on ${n}$ vertices equipped with uniformly heavy edge weights and use iteration methods to obtain deviation…

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

Hypernetworks, or hypernets for short, are neural networks that generate weights for another neural network, known as the target network. They have emerged as a powerful deep learning technique that allows for greater flexibility,…

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…

We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by…

Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…