Related papers: On Spectral Analysis of Directed Signed Graphs
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to…
We apply a novel spectral graph technique, that of locally-biased semi-supervised eigenvectors, to study the diversity of galaxies. This technique permits us to characterize empirically the natural variations in observed spectra data, and…
Massive network exploration is an important research direction with many applications. In such a setting, the network is, usually, modeled as a graph $G$, whereas any structural information of interest is extracted by inspecting the way…
Scene understanding has been of high interest in computer vision. It encompasses not only identifying objects in a scene, but also their relationships within the given context. With this goal, a recent line of works tackles 3D semantic…
Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs to represent social interactions,…
Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…
A fundamental problem in mathematics and network analysis is to find conditions under which a graph can be partitioned into smaller pieces. The most important tool for this partitioning is the Fiedler vector or discrete Cheeger inequality.…
In graph property testing the task is to distinguish whether a graph satisfies a given property or is "far" from having that property, preferably with a sublinear query and time complexity. In this work we initiate the study of property…
Signed graphs are powerful models for representing complex relations with both positive and negative connections. Recently, Signed Graph Neural Networks (SGNNs) have emerged as potent tools for analyzing such graphs. To our knowledge, no…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
Graph Neural Networks (GNNs) have received increasing attention in many fields. However, due to the lack of prior graphs, their use for semantic labeling has been limited. Here, we propose a novel architecture called the Self-Constructing…
The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
Autoencoders based on Graph Neural Networks (GNNs) have garnered significant attention in recent years for their ability to extract informative latent representations, characterizing the structure of complex topologies, such as graphs.…
Hypergraph spectral analysis has emerged as an effective tool processing complex data structures in data analysis. The surface of a three-dimensional (3D) point cloud and the multilateral relationship among their points can be naturally…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…