Related papers: Structure from Voltage
Graph auto-encoders have proved to be useful in network embedding task. However, current models only consider explicit structures and fail to explore the informative latent structures cohered in networks. To address this issue, we propose a…
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…
Exponential family Random Graph Models (ERGMs) can be viewed as expressing a probability distribution on graphs arising from the action of competing social forces that make ties more or less likely, depending on the state of the rest of the…
This paper characterizes the graphical properties of an optimal topology with minimal Laplacian energy under the constraint of fixed numbers of vertices and edges, and devises an algorithm to construct such connected optimal graphs. These…
We address the Laplacian on a perturbed periodic graph which might not be a periodic graph. We present a class of perturbed graphs for which the essential spectra of the Laplacians are stable even when the graphs are perturbed by adding and…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles…
Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
Resistance distance is a novel distance function, also a new intrinsic graph metric, which makes some extensions of ordinary distance. Let On be a linear crossed octagonal graph. Recently, Pan and Li (2018) derived the closed formulas for…
For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. In addition to studying these matrices, several related structures are…
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances. In this…
With the development of quantum algorithms, high-cost computations are being scrutinized in the hope of a quantum advantage. While graphs offer a convenient framework for multiple real-world problems, their analytics still comes with high…
Resistance distance computation is a fundamental problem in graph analysis, yet existing random walk-based methods are limited to approximate solutions and suffer from poor efficiency on small-treewidth graphs (e.g., road networks). In…
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in $O(1)$ time. Moreover, it can report…
In this paper, we use graph theory to solve wave scattering problems in the discrete dipole approximation. As a key result of this work, in the presence of active scatterers, we present a systematic method to find arbitrary large-order zero…
Edge-labeled graphs are widely used to describe relationships between entities in a database. Given a query subgraph that represents an example of what the user is searching for, we study the problem of efficiently searching for similar…
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…