相关论文: Finding the Cores of Higher Graphs Using Geometric…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

The value of graph-based big data can be unlocked by exploring the topology and metrics of the networks they represent, and the computational approaches to this exploration take on many forms. The use-case of performing global computations…

An ordered graph is a graph enhanced with a linear order on the vertex set. An ordered graph is a core if it does not have an order-preserving homomorphism to a proper subgraph. We say that $H$ is the core of $G$ if (i) $H$ is a core, (ii)…

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We…

Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…

Massive network exploration is an important research direction with many applications. In such a setting, the network is, usually, modeled as a graph $G$, whereas any structural information of interest is extracted by inspecting the way…

We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…

Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…

Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…

In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…

Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have been invented. In this paper, we give some algorithms to…

We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…

We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the first definition of map homomorphism that preserves both the…

The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…

Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…

We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for {\em graphs with semi-edges}. The notion of graph covering is a discretization of coverings between surfaces or topological…