Related papers: Spectral density of random graphs: convergence pro…
Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and…
Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Networks describe the, often complex, relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a dataset well…
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…
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…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…
We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual…
A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…
We study the spectral properties of the process of explosive percolation. In particular, we explore how the maximum eigenvalue of the adjacency matrix of a network which governs the spreading efficiency evolves as the density of connection…
Graph Representation Learning (GRL) has experienced significant progress as a means to extract structural information in a meaningful way for subsequent learning tasks. Current approaches including shallow embeddings and Graph Neural…
This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals…
We introduce a new spectral method for image segmentation that incorporates long range relationships for global appearance modeling. The approach combines two different graphs, one is a sparse graph that captures spatial relationships…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…