Graph Set-colorings And Hypergraphs In Topological Coding

• URL: http://arxiv.org/abs/2201.13354v2
• Date: Wed, 17 Apr 2024 16:42:04 GMT
• Title: Graph Set-colorings And Hypergraphs In Topological Coding
• Authors: Bing Yao, Fei Ma,
• Abstract summary: We will introduce set-colored graphs admitting set-colorings that has been considerable cryptanalytic significance. We use the set-coloring of graphs to reflect the intersection of elements, and add other constraint requirements to express more connections between sets (as hyperedges)
• Score: 8.142947808507367
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 introduce set-colored graphs admitting set-colorings that has been considerable cryptanalytic significance, and especially related with hypergraphs. We use the set-coloring of graphs to reflect the intersection of elements, and add other constraint requirements to express more connections between sets (as hyperedges). Since we try to find some easy and effective techniques based on graph theory for practical application, we use intersected-graphs admitting set-colorings defined on hyperedge sets to observe topological structures of hypergraphs, string-type Topcode-matrix, set-type Topcode-matrix, graph-type Topcode-matrix, hypergraph-type Topcode-matrix, matrix-type Topcode-matrix \emph{etc}. We will show that each connected graph is the intersected-graph of some hypergraph and investigate hypergraph's connectivity, colorings of hypergraphs, hypergraph homomorphism, hypernetworks, scale-free network generator, compound hypergraphs having their intersected-graphs with vertices to be hypergraphs (for high-dimensional extension diagram). Naturally, we get various graphic lattices, such as edge-coincided intersected-graph lattice, vertex-coincided intersected-graph lattice, edge-hamiltonian graphic lattice, hypergraph lattice and intersected-network lattice. Many techniques in this article can be translated into polynomial algorithms, since we are aiming to apply hypergraphs and graph set-colorings to homomorphic encryption and asymmetric cryptograph.

Related papers

• UniG-Encoder: A Universal Feature Encoder for Graph and Hypergraph Node Classification [6.977634174845066]
  A universal feature encoder for both graph and hypergraph representation learning is designed, called UniG-Encoder. The architecture starts with a forward transformation of the topological relationships of connected nodes into edge or hyperedge features. The encoded node embeddings are then derived from the reversed transformation, described by the transpose of the projection matrix.
  arXiv  Detail & Related papers  (2023-08-03T09:32:50Z)
• From Hypergraph Energy Functions to Hypergraph Neural Networks [94.88564151540459]
  We present an expressive family of parameterized, hypergraph-regularized energy functions. We then demonstrate how minimizers of these energies effectively serve as node embeddings. We draw parallels between the proposed bilevel hypergraph optimization, and existing GNN architectures in common use.
  arXiv  Detail & Related papers  (2023-06-16T04:40:59Z)
• Graph Mixup with Soft Alignments [49.61520432554505]
  We study graph data augmentation by mixup, which has been used successfully on images. We propose S-Mixup, a simple yet effective mixup method for graph classification by soft alignments.
  arXiv  Detail & Related papers  (2023-06-11T22:04:28Z)
• All the World's a (Hyper)Graph: A Data Drama [55.144729234861316]
  Hyperbard is a dataset of diverse data representations from Shakespeare's plays. Our representations range from simple graphs capturing character co-occurrence in single scenes to hypergraphs encoding complex communication settings. As an homage to our data source, and asserting that science can also be art, we present all our points in the form of a play.
  arXiv  Detail & Related papers  (2022-06-16T14:51:28Z)
• Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs [59.71134113268709]
  We present General Hypergraph Spectral Convolution(GHSC), a general learning framework that can handle EDVW and EIVW hypergraphs. In this paper, we show that the proposed framework can achieve state-of-the-art performance. Experiments from various domains including social network analysis, visual objective classification, protein learning demonstrate that the proposed framework can achieve state-of-the-art performance.
  arXiv  Detail & Related papers  (2022-03-31T10:46:47Z)
• HyperSF: Spectral Hypergraph Coarsening via Flow-based Local Clustering [9.438207505148947]
  We propose an efficient spectral hypergraph coarsening scheme (HyperSF) for preserving the original spectral (structural) properties of hypergraphs. Our results show that the proposed hypergraph coarsening algorithm can significantly improve the multi-way conductance of hypergraph clustering.
  arXiv  Detail & Related papers  (2021-08-17T22:20:23Z)
• Edge Representation Learning with Hypergraphs [36.03482700241067]
  We propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance. Our edge representation learning and pooling method also largely outperforms state-of-the-art graph pooling methods on graph classification.
  arXiv  Detail & Related papers  (2021-06-30T06:59:05Z)
• NetVec: A Scalable Hypergraph Embedding System [1.8979377273990425]
  We introduce NetVec, a novel framework for scalable un-supervised hypergraph embedding. We show that NetVec can becoupled with any graph embedding algorithm to produce embeddings of hypergraphs with millionsof nodes and hyperedges in a few minutes.
  arXiv  Detail & Related papers  (2021-03-09T18:06:56Z)
• Inverse Graph Identification: Can We Identify Node Labels Given Graph Labels? [89.13567439679709]
  Graph Identification (GI) has long been researched in graph learning and is essential in certain applications. This paper defines a novel problem dubbed Inverse Graph Identification (IGI) We propose a simple yet effective method that makes the node-level message passing process using Graph Attention Network (GAT) under the protocol of GI.
  arXiv  Detail & Related papers  (2020-07-12T12:06:17Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)
• Line Hypergraph Convolution Network: Applying Graph Convolution for Hypergraphs [18.7475578342125]
  We propose a novel technique to apply graph convolution on hypergraphs with variable hyperedge sizes. We use the classical concept of line graph of a hypergraph for the first time in the hypergraph learning literature.
  arXiv  Detail & Related papers  (2020-02-09T16:05:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.