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In this paper we investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which admit a compact semigroup topology and describe graph…

Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…

In this paper we raise the question of how to compress sparse graphs. By introducing the idea of redundancy, we find a way to measure the overlap of neighbors between nodes in networks. We exploit symmetry and information by making use of…

Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…

Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be…

We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…

Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…

Constantly growing demands of high productivity and security of computer systems and computer networks call the interest of specialists in the environment of construction of optimum topologies of computer mediums. In earliest phases of…

Graph representations of solid state materials that encode only interatomic distance lack geometrical resolution, resulting in degenerate representations that may map distinct structures to equivalent graphs. Here we propose a hypergraph…

Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel…

Graph embedding techniques have attracted growing interest since they convert the graph data into continuous and low-dimensional space. Effective graph analytic provides users a deeper understanding of what is behind the data and thus can…

Graph embedding, aiming to learn low-dimensional representations (aka. embeddings) of nodes, has received significant attention recently. Recent years have witnessed a surge of efforts made on static graphs, among which Graph Convolutional…

Unit disk graphs are the intersection graphs of unit radius disks in the Euclidean plane. Deciding whether there exists an embedding of a given unit disk graph, i.e. unit disk graph recognition, is an important geometric problem, and has…

Network embedding techniques aim at representing structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph…

Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges,…

Small interconnected quantum processors can collaborate to tackle quantum computational problems that typically demand more capable devices. These linked processors, referred to as quantum nodes, can use shared entangled states to execute…

In this contribution we consider an advantageous building block with potential for various quantum applications: a device based on coupled spins capable of generating and sharing out an entangled pair of qubits. Our model device is a…

Many inference tasks on knowledge graphs, including relation prediction, operate on knowledge graph embeddings -- vector representations of the vertices (entities) and edges (relations) that preserve task-relevant structure encoded within…

Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…