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Network embedding is aimed at mapping nodes in a network into low-dimensional vector representations. Graph Neural Networks (GNNs) have received widespread attention and lead to state-of-the-art performance in learning node representations.…
A fundamental theorem of Laman characterises when a bar-joint framework realised generically in the Euclidean plane admits a non-trivial continuous deformation of its vertices. This has recently been extended in two ways. Firstly to…
How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…
We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this…
Global Navigation Satellite Systems (GNSS) are a widely used technology for positioning and navigation. GNSS positioning relies on pseudorange measurements from satellites to receivers. A pseudorange is the apparent distance between two…
Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based…
A set $D$ of vertices of a graph is a \emph{defensive alliance} if, for each element of $D$, the majority of its neighbours are in $D$. We consider the notion of local minimality in this paper. We are interested in finding a locally minimal…
We study the rigidity results for self-shrinkers in Euclidean space by restriction of the image under the Gauss map. The geometric properties of the target manifolds carry into effect. In the self-shrinking hypersurface situation Theorem…
Graph-based representations such as Scene Graphs enable localization in structured indoor environments by matching a locally observed graph, constructed from sensor data, to a prior map. This process is particularly challenging in…
Graph Neural Networks (GNNs) have achieved notable success in learning from graph-structured data, owing to their ability to capture intricate dependencies and relationships between nodes. They excel in various applications, including…
Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the…
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.…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization.…
A signed directed graph is a graph with sign and direction information on the edges. Even though signed directed graphs are more informative than unsigned or undirected graphs, they are more complicated to analyze and have received less…
Multi-agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-agent network to perturbations such as failures, noise, or malicious…
Traditional network analysis focuses on binary edges, while real-world relationships are more nuanced, encompassing cooperation, neutrality, and conflict. The rise of negative edges in social media discussions spurred interest in analyzing…
In this paper, we will give a structure theory for signed graphs with fixed smallest eigenvalue and investigate signed graphs with smallest eigenvalue greater than $-1-\sqrt{2}$. Given a real number $\lambda\leq -1$, we show that the…
It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…