Related papers: A Generative Model for Controllable Feature Hetero…

Graph neural networks (GNNs) have demonstrated superior performance for semi-supervised node classification on graphs, as a result of their ability to exploit node features and topological information simultaneously. However, most GNNs…

We propose a novel graph-driven generative model, that unifies multiple heterogeneous learning tasks into the same framework. The proposed model is based on the fact that heterogeneous learning tasks, which correspond to different…

A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a…

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely…

We investigate the representation power of graph neural networks in the semi-supervised node classification task under heterophily or low homophily, i.e., in networks where connected nodes may have different class labels and dissimilar…

While heterophily has been widely studied in node-level tasks, its impact on graph-level tasks remains unclear. We present the first analysis of heterophily in graph-level learning, combining theoretical insights with empirical validation.…

In this paper, we investigate the controllability of a linear time-invariant network following a Laplacian dynamics defined on a threshold graph. In this direction, an algorithm for deriving the modal matrix associated with the Laplacian…

Graphons, as limits of graph sequences, provide an operator-theoretic framework for analyzing the asymptotic behavior of graph neural operators. Spectral convergence of sampled graphs to graphons induces convergence of the corresponding…

Graph neural networks (GNNs) have emerged as a powerful tool for modeling graph-structured data. However, existing GNNs often struggle with heterophilic graphs, where connected nodes tend to have dissimilar features or labels. While…

Graph Neural Networks (GNNs) have received increasing attention for representation learning in various machine learning tasks. However, most existing GNNs applying neighborhood aggregation usually perform poorly on the graph with…

This paper studies the Laplacian spectrum and the average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is that the Laplacian eigenvalues of a large dense graph can be effectively…

Graph Neural Networks (GNNs) have become pivotal tools for a range of graph-based learning tasks. Notably, most current GNN architectures operate under the assumption of homophily, whether explicitly or implicitly. While this underlying…

Structure aware graph generation aims to generate graphs that satisfy given topological properties. It has applications in domains such as drug discovery, social network modeling, and knowledge graph construction. Unlike existing methods…

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…

When each data point is a large graph, graph statistics such as densities of certain subgraphs (motifs) can be used as feature vectors for machine learning. While intuitive, motif counts are expensive to compute and difficult to work with…

Graph neural networks (GNNs) based methods have achieved impressive performance on node clustering task. However, they are designed on the homophilic assumption of graph and clustering on heterophilic graph is overlooked. Due to the lack of…

Graph Laplacian learning, also known as network topology inference, is a problem of great interest to multiple communities. In Gaussian graphical models (GM), graph learning amounts to endowing covariance selection with the Laplacian…

In the past, the dichotomy between homophily and heterophily has inspired research contributions toward a better understanding of Deep Graph Networks' inductive bias. In particular, it was believed that homophily strongly correlates with…

Social networks have a small number of large hubs, and a large number of small dense communities. We propose a generative model that captures both hub and dense structures. Based on recent results about graphons on line graphs, our model is…

We develop a theory of ultrametric graphons as limiting objects for random networks with nested hierarchical community structure. A graphon $W:[0,1]^2\to[0,1]$ is called ultrametric if $W(x,y)=w(d(x,y))$, where $d$ is an ultrametric on…