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Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…
Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hierarchy. Consequently, Persistent Homology (PH) methods are…
We study the problem of determining the optimal low dimensional projection for maximising the separability of a binary partition of an unlabelled dataset, as measured by spectral graph theory. This is achieved by finding projections which…
With recent advancements in graph neural networks (GNNs), spectral GNNs have received increasing popularity by virtue of their ability to retrieve graph signals in the spectral domain. These models feature uniqueness in efficient…
Hybrid light fidelity (LiFi) and wireless fidelity (WiFi) networks are a promising paradigm of heterogeneous network (HetNet), attributed to the complementary physical properties of optical spectra and radio frequency. However, the current…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
Overlay network topology together with peer/data organization and search algorithm are the crucial components of unstructured peer-to-peer (P2P) networks as they directly affect the efficiency of search on such networks. Scale-free…
Let $\lambda_{1}(G)$ and $\mu_{1}(G)$ denote the spectral radius and the Laplacian spectral radius of a graph $G$, respectively. Li in [Electronic J. Linear Algebra 34 (2018) 389-392] proved sharp upper bounds of $\lambda_{1}(G)$ based on…
The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…
This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…
Pruning-at-Initialization (PaI) algorithms provide Sparse Neural Networks (SNNs) which are computationally more efficient than their dense counterparts, and try to avoid performance degradation. While much emphasis has been directed towards…
Can integrating spectral and curvature signals unlock new potential in graph representation learning? Non-Euclidean geometries, particularly Riemannian manifolds such as hyperbolic (negative curvature) and spherical (positive curvature),…
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total…
A statistician designing an experiment wants to get as much information as possible from the data gathered. Often this means the most precise estimate possible (that is, an estimate with minimum possible variance) of the unknown parameters.…
Graph neural networks (GNNs) have been widely applied in traffic demand prediction, and transportation modes can be divided into station-based mode and free-floating traffic mode. Existing research in traffic graph construction primarily…
The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where…
Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then…
We propose that clusters interconnected with network topologies having minimal mean path length will increase their overall performance for a variety of applications. We approach our heuristic by constructing clusters of up to 36 nodes…