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Graph contrastive learning (GCL) has recently emerged as an effective learning paradigm to alleviate the reliance on labelling information for graph representation learning. The core of GCL is to maximise the mutual information between the…
Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization,…
Graph-structured data are pervasive in the real-world such as social networks, molecular graphs and transaction networks. Graph neural networks (GNNs) have achieved great success in representation learning on graphs, facilitating various…
In this paper, we introduce a connection between two classical concepts of graph theory: \; metric dimension and distinguishing number. For a given graph $G$, let ${\rm dim}(G)$ and $D(G)$ represent its metric dimension and distinguishing…
The symmetric difference of two graphs $G_1,G_2$ on the same set of vertices $V$ is the graph on $V$ whose set of edges are all edges that belong to exactly one of the two graphs $G_1,G_2$. For a fixed graph $H$ call a collection ${\cal G}$…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
Graph neural network (GNN) has gained increasing popularity in recent years owing to its capability and flexibility in modeling complex graph structure data. Among all graph learning methods, hypergraph learning is a technique for exploring…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
Graph Contrastive Learning (GCL) has recently drawn much research interest for learning generalizable node representations in a self-supervised manner. In general, the contrastive learning process in GCL is performed on top of the…
This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…
We study differential privacy (DP) in a multi-party setting where each party only trusts a (known) subset of the other parties with its data. Specifically, given a trust graph where vertices correspond to parties and neighbors are mutually…
Graph neural networks (GNNs) are important tools for transductive learning tasks, such as node classification in graphs, due to their expressive power in capturing complex interdependency between nodes. To enable graph neural network…
Based on \cite{DH94}, we introduce a bijective correspondence between first order differential calculi and the graph structure of the symmetric lattice that allows one to encode completely the interconnection structure of the graph in the…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
Graph convolutional networks (GCNs) are a powerful architecture for representation learning on documents that naturally occur as graphs, e.g., citation or social networks. However, sensitive personal information, such as documents with…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
A subset $S$ of vertices of a connected graph $G$ is a distance-equalizer set if for every two distinct vertices $x, y \in V (G) \setminus S$ there is a vertex $w \in S$ such that the distances from $x$ and $y$ to $w$ are the same. The…
A (Euclidean) greedy drawing of a graph is a drawing in which, for any two vertices $s,t$ ($s \neq t$), there is a neighbor vertex of $s$ that is closer to $t$ than to $s$ in the Euclidean distance. Greedy drawings are important in the…
Graph learning plays a vital role in mining and analyzing complex relationships within graph data and has been widely applied to real-world scenarios such as social, citation, and e-commerce networks. Foundation models in computer vision…
This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…