相关论文: On the Construction of Singular and Cospectral Hyp…

For a connected graph $G$, we present the concept of a new graph matrix related to its distance and Seidel matrix, called distance Seidel matrix $\mathcal{D}^S(G)$. Suppose that the eigenvalues of $\mathcal{D}^S(G)$ be $\partial_{1}^{S}(G)…

This paper presents a multiscale graph construction method using both graph and signal features. Multiscale graph is a hierarchical representation of the graph, where a node at each level indicates a cluster in a finer resolution. To obtain…

Graph Neural Networks (GNNs) are gaining increasing attention on graph data learning tasks in recent years. However, in many applications, graph may be coming in an incomplete form where attributes of graph nodes are partially…

Graph-based semi-supervised node classification has been shown to become a state-of-the-art approach in many applications with high research value and significance. Most existing methods are only based on the original intrinsic or…

Graph Neural Networks (GNNs) learn low dimensional representations of nodes by aggregating information from their neighborhood in graphs. However, traditional GNNs suffer from two fundamental shortcomings due to their local ($l$-hop…

A graph G is an NG-graph if \chi(G) + \chi(G complement) = |V(G)| + 1. We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm. We also explore the connections between NG-graphs and split…

We introduce a hypergraph matrix, named the unified matrix, and use it to represent the hypergraph as a graph. We show that the unified matrix of a hypergraph is identical to the adjacency matrix of the associated graph. This enables us to…

A graph is said to be NSSD (= non-singular with a singular deck) if it has no eigenvalue equal to zero, whereas all its vertex-deleted subgraphs have eigenvalues equal to zero. NSSD graphs are of importance in the theory of conductance of…

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…

Deep graph clustering (DGC), which aims to unsupervisedly separate the nodes in an attribute graph into different clusters, has seen substantial potential in various industrial scenarios like community detection and recommendation. However,…

Recent research on graph neural networks (GNNs) has explored mechanisms for capturing local uncertainty and exploiting graph hierarchies to mitigate data sparsity and leverage structural properties. However, the synergistic integration of…

Recent years have witnessed the popularity and success of graph neural networks (GNN) in various scenarios. To obtain data-specific GNN architectures, researchers turn to neural architecture search (NAS), which has made impressive success…

Graph Neural Networks (GNNs) have demonstrated impressive performance across diverse graph-based tasks by leveraging message passing to capture complex node relationships. However, on large-scale real-world graphs, GNNs face two major…

A Not-All-Equal (NAE) decomposition of a graph $G$ is a decomposition of the vertices of $G$ into two parts such that each vertex in $G$ has at least one neighbor in each part. Also, a 1-in-Degree decomposition of a graph $G$ is a…

Let R be a commutative ring and M be an R-module. We define the large sum graph, denoted by \acute{G}(M), as a graph with the vertex set of non-large submodules of M and two distinct vertices are adjacent if and only if N + K is a non-large…

Graph neural networks (GNNs) have demonstrated promising performance across various chemistry-related tasks. However, conventional graphs only model the pairwise connectivity in molecules, failing to adequately represent higher-order…

The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lov\'asz (1974)…

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming…

A $k$-regular graph on $v$ vertices is a {\em divisible design graph} if there exist integers $\lambda_1,\lambda_2,m,n$ such that the vertex set can be partitioned into $m$ classes of size $n$ and any two different vertices from the same…

In this paper we describe an extension of the Variable Neighbourhood Search (VNS) which integrates the basic VNS with other complementary approaches from machine learning, statistics and experimental algorithmic, in order to produce…