Related papers: Improving Expressive Power of Spectral Graph Neura…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
To some extent, graph evolutionary mechanisms can be explained by its spectra. Here, we are interested in two graph operations, namely, motif (subgraph) doubling and attachment that are biologically relevant. We investigate how these two…
We undertake an extensive numerical investigation of the graph spectra of thousands regular graphs, a set of random Erd\"os-R\'enyi graphs, the two most popular types of complex networks and an evolving genetic network by using novel…
Whilst spectral Graph Neural Networks (GNNs) are theoretically well-founded in the spectral domain, their practical reliance on polynomial approximation implies a profound linkage to the spatial domain. As previous studies rarely examine…
Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
Graph representation learning has become a standard approach for analyzing networked data, with latent embeddings widely used for link prediction, community detection, and related tasks. Yet a basic design choice, the latent dimension, is…
In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power…
The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to…
The core operation of current Graph Neural Networks (GNNs) is the aggregation enabled by the graph Laplacian or message passing, which filters the neighborhood node information. Though effective for various tasks, in this paper, we show…
Graph Neural Networks (GNNs) have emerged as a powerful tool for learning on graph-structured data, finding applications in numerous domains including social network analysis and molecular biology. Within this broad category, Asynchronous…
Based on matrix perturbation theory, closed-form analytic expansions are studied for a Laplacian eigenvalue of an undirected, possibly weighted graph, which is close to a unique degree in that graph. An approximation is presented to provide…
Graph convolutional networks (GCNs) have achieved remarkable learning ability for dealing with various graph structural data recently. In general, deep GCNs do not work well since graph convolution in conventional GCNs is a special form of…
Message passing Graph Neural Networks (GNNs) are known to be limited in expressive power by the 1-WL color-refinement test for graph isomorphism. Other more expressive models either are computationally expensive or need preprocessing to…
Graph Neural Networks (GNNs) excel in handling graph-structured data but often underperform in link prediction tasks compared to classical methods, mainly due to the limitations of the commonly used message-passing principle. Notably, their…
We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated…
Spectral Graph Neural Networks have demonstrated superior performance in graph representation learning. However, many current methods focus on employing shared polynomial coefficients for all nodes, i.e., learning node-unified filters,…
We define a graph to be $S$-regular if it contains an equitable partition given by a matrix $S$. These graphs are generalizations of both regular and bipartite, biregular graphs. An $S$-regular matrix is defined then as a matrix on an…
Graphs are central to modeling complex systems in domains such as social networks, molecular chemistry, and neuroscience. While Graph Neural Networks, particularly Graph Convolutional Networks, have become standard tools for graph learning,…