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The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
Fast and reliable optimal power flow (OPF) approximation is essential for reliable smart-grid operation, yet many learning-based surrogates either flatten the native heterogeneous structure of power networks, target a limited set of grid…
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.…
We study the spectral gap of the Erd\H{o}s--R\'enyi random graph through the connectivity threshold. In particular, we show that for any fixed $\delta > 0$ if $$p \ge \frac{(1/2 + \delta) \log n}{n},$$ then the normalized graph Laplacian of…
The performance of large-scale computing systems often critically depends on high-performance communication networks. Dynamically reconfigurable topologies, e.g., based on optical circuit switches, are emerging as an innovative new…
We present experimental results and a user study for hierarchical drawings of graphs. A detailed hierarchical graph drawing technique that is based on the Path Based Framework (PBF) is presented. Extensive edge bundling is applied to draw…
Developing deep learning models with strong adaptability to topological variations is of great practical significance for power flow analysis. To enhance model performance under variable system scales and improve robustness in branch power…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Recent years have witnessed the promise that reinforcement learning, coupled with Graph Neural Network (GNN) architectures, could learn to solve hard combinatorial optimization problems: given raw input data and an evaluator to guide the…
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $\epsilon$-graphs and $k$-NN graphs can lead to poor performance…
A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have…
We consider the routing of neutral atoms on a reconfigurable lattice in terms of hypergraph transformations. We prove the routing number of a Ramanujan $(d,r)$-regular hypergraph on $N$ vertices satisfies $\mathrm{rt}(H) = \Theta(\log N)$,…
Spectral graph theory has been widely applied in unsupervised and semi-supervised learning. In this paper, we find for the first time, to our knowledge, that it also plays a concrete role in supervised classification. It turns out that two…
Unmanned Aerial Vehicles (UAVs) hold great potential to support a wide range of applications due to the high maneuverability and flexibility. Compared with single UAV, UAV swarm carries out tasks efficiently in harsh environment, where the…
In a paper by Nishikawa and Motter, a quantity called the normalized spread of the Laplacian eigenvalues is used to measure the synchronizability of certain network dynamics. Through simulations, and without theoretical validation, it is…
We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…
In this paper we study spectral properties of graphs which are constructed from two given invertible graphs by bridging them over a bipartite graph. We analyze the so-called HOMO-LUMO spectral gap which is the difference between the…
Low-diameter topologies such as Dragonfly and Slim Fly are increasingly adopted in HPC and datacenter networks, yet existing load balancing techniques either rely on proprietary in-network mechanisms or fail to utilize the full path…
Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly…
We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the…