相关论文: Statistical properties of a generalized threshold …
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…
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…
In epidemic modeling, the term infection strength indicates the ratio of infection rate and cure rate. If the infection strength is higher than a certain threshold -- which we define as the epidemic threshold - then the epidemic spreads…
An important source of high clustering coefficient in real-world networks is transitivity. However, existing approaches for modeling transitivity suffer from at least one of the following problems: i) they produce graphs from a specific…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp {[}-\beta \H(\c)…
The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by…
In previous papers, threshold probabilities for the properties of a random distance graph to contain strictly balanced graphs were found. We extend this result to arbitrary graphs and prove that the number of copies of a strictly balanced…
In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad-hoc networks "soft" or "probabilistic"…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…
Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…