Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to cert...Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.展开更多
This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh ...This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh principle and the perturbation of the spectral radius under moving the edge operation,and the extremal hypergraphs are characterized for both supertree and unicyclic hypergraphs.The spectral radius of the graph is generalized.展开更多
Practical real-world scenarios such as the Internet,social networks,and biological networks present the challenges of data scarcity and complex correlations,which limit the applications of artificial intelligence.The ...Practical real-world scenarios such as the Internet,social networks,and biological networks present the challenges of data scarcity and complex correlations,which limit the applications of artificial intelligence.The graph structure is a typical tool used to formulate such correlations,it is incapable of modeling highorder correlations among different objects in systems;thus,the graph structure cannot fully convey the intricate correlations among objects.Confronted with the aforementioned two challenges,hypergraph computation models high-order correlations among data,knowledge,and rules through hyperedges and leverages these high-order correlations to enhance the data.Additionally,hypergraph computation achieves collaborative computation using data and high-order correlations,thereby offering greater modeling flexibility.In particular,we introduce three types of hypergraph computation methods:①hypergraph structure modeling,②hypergraph semantic computing,and③efficient hypergraph computing.We then specify how to adopt hypergraph computation in practice by focusing on specific tasks such as three-dimensional(3D)object recognition,revealing that hypergraph computation can reduce the data requirement by 80%while achieving comparable performance or improve the performance by 52%given the same data,compared with a traditional data-based method.A comprehensive overview of the applications of hypergraph computation in diverse domains,such as intelligent medicine and computer vision,is also provided.Finally,we introduce an open-source deep learning library,DeepHypergraph(DHG),which can serve as a tool for the practical usage of hypergraph computation.展开更多
Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important n...Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important nodes in a directed hypergraph.The algorithm introduces the Jaccard similarity of directed hypergraphs.By comparing the numbers of common neighbors between nodes with the total number of their neighbors,the Jaccard similarity measure takes into account the similarity between nodes that are not directly connected,and can reflect the potential correlation between nodes.An improved susceptible–infected(SI)model in directed hypergraph is proposed,which considers nonlinear propagation mode and more realistic propagation mechanism.In addition,some important node evaluation methods are transferred from undirected hypergraphs and applied to directed hypergraphs.Finally,the ImPageRank algorithm is used to evaluate the performance of the SI model,network robustness and monotonicity.Simulations of real networks demonstrate the excellent performance of the proposed algorithm and provide a powerful framework for identifying important nodes in directed hypergraphs.展开更多
Complex networks play a crucial role in the study of collective behavior,encompassing the analysis of dynamical properties and network topology.In real-world systems,higher-order interactions among multiple entities a...Complex networks play a crucial role in the study of collective behavior,encompassing the analysis of dynamical properties and network topology.In real-world systems,higher-order interactions among multiple entities are widespread and significantly influence collective dynamics.Here,we extend the synchronization alignment function framework to hypergraphs of arbitrary order by leveraging the multi-order Laplacian matrix to encode higher-order interactions.Our findings reveal that the upper bound of synchronous behavior is determined by the maximum eigenvalue of the multi-order Laplacian matrix.Furthermore,we decompose the contribution of each hyperedge to this eigenvalue and utilize it as a basis for designing an eigenvalue-based topology modification algorithm.This algorithm effectively enhances the upper bound of synchronous behavior without altering the total number of higher-order interactions.Our study provides new insights into dynamical optimization and topology tuning in hypergraphs,advancing the understanding of the interplay between higher-order interactions and collective dynamics.展开更多
Traffic flow prediction is a crucial element of intelligent transportation systems.However,accu-rate traffic flow prediction is quite challenging because of its highly nonlinear,complex,and dynam-ic characteristics.To...Traffic flow prediction is a crucial element of intelligent transportation systems.However,accu-rate traffic flow prediction is quite challenging because of its highly nonlinear,complex,and dynam-ic characteristics.To address the difficulties in simultaneously capturing local and global dynamic spatiotemporal correlations in traffic flow,as well as the high time complexity of existing models,a multi-head flow attention-based local-global dynamic hypergraph convolution(MFA-LGDHC)pre-diction model is proposed.which consists of multi-head flow attention(MHFA)mechanism,graph convolution network(GCN),and local-global dynamic hypergraph convolution(LGHC).MHFA is utilized to extract the time dependency of traffic flow and reduce the time complexity of the model.GCN is employed to catch the spatial dependency of traffic flow.LGHC utilizes down-sampling con-volution and isometric convolution to capture the local and global spatial dependencies of traffic flow.And dynamic hypergraph convolution is used to model the dynamic higher-order relationships of the traffic road network.Experimental results indicate that the MFA-LGDHC model outperforms current popular baseline models and exhibits good prediction performance.展开更多
This paper mainly studies the influence maximization problem of threshold models in hypergraphs,which aims to identify the most influential nodes in hypergraphs.Firstly,we introduce a novel information diffusion rule ...This paper mainly studies the influence maximization problem of threshold models in hypergraphs,which aims to identify the most influential nodes in hypergraphs.Firstly,we introduce a novel information diffusion rule in hypergraphs based on Threshold Models and conduct the stability analysis.Then we extend the CI-TM algorithm,originally designed for complex networks,to hypergraphs,denoted as the H-CI-TM algorithm.Secondly,we use an iterative approach to get the globally optimal solutions.The analysis reveals that our algorithm ultimately identifies the most influential set of nodes.Based on the numerical simulations,HCI-TM algorithm outperforms several competing algorithms in both synthetic and real-world hypergraphs.Essentially,when provided with the same number of initial seeds,our algorithm can achieve a larger activation size.Our method not only accurately assesses the influence of individual nodes but also identifies a set of nodes with greater impact.Furthermore,our results demonstrate good scalability when handling intricate relationships and large-scale hypergraphs.The outcomes of our research provide substantial support for the applications of the threshold models across diverse fields,including social network analysis and marketing strategies.展开更多
The existing multi-view subspace clustering algorithms based on tensor singular value decomposition(t-SVD)predominantly utilize tensor nuclear norm to explore the intra view correlation between views of the same sampl...The existing multi-view subspace clustering algorithms based on tensor singular value decomposition(t-SVD)predominantly utilize tensor nuclear norm to explore the intra view correlation between views of the same samples,while neglecting the correlation among the samples within different views.Moreover,the tensor nuclear norm is not fully considered as a convex approximation of the tensor rank function.Treating different singular values equally may result in suboptimal tensor representation.A hypergraph regularized multi-view subspace clustering algorithm with dual tensor log-determinant(HRMSC-DTL)was proposed.The algorithm used subspace learning in each view to learn a specific set of affinity matrices,and introduced a non-convex tensor log-determinant function to replace the tensor nuclear norm to better improve global low-rankness.It also introduced hyper-Laplacian regularization to preserve the local geometric structure embedded in the high-dimensional space.Furthermore,it rotated the original tensor and incorporated a dual tensor mechanism to fully exploit the intra view correlation of the original tensor and the inter view correlation of the rotated tensor.At the same time,an alternating direction of multipliers method(ADMM)was also designed to solve non-convex optimization model.Experimental evaluations on seven widely used datasets,along with comparisons to several state-of-the-art algorithms,demonstrated the superiority and effectiveness of the HRMSC-DTL algorithm in terms of clustering performance.展开更多
An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is ...An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.展开更多
A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower tha...A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower than that of ECP method in several order of magnitude.展开更多
We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G =...We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G = (V, E), its rupture degree r(G<sup>k</sup>) is defined as r(G<sup>k</sup>) = max{ω(G<sup>k</sup> - X) - |X| - m(G<sup>k</sup> - X): X <span style="white-space:nowrap;">⊂ V(G<sup>k</sup>), ω(G<sup>k</sup> - X) > 1}, where X is a cut set (or destruction strategy) of G<sup>k</sup>, ω(G<sup>k</sup> - X) and m(G<sup>k</sup> - X) denote the number of components and the order of a largest component in G<sup>k</sup> - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.展开更多
The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decompos...The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.展开更多
The product functional confguration(PFC)is typically used by frms to satisfy the individual requirements of customers and is realized based on market analysis.This study aims to help frms analyze functions and realize...The product functional confguration(PFC)is typically used by frms to satisfy the individual requirements of customers and is realized based on market analysis.This study aims to help frms analyze functions and realize functional confgurations using patent data.This study frst proposes a patent-data-driven PFC method based on a hypergraph network.It then constructs a weighted network model to optimize the combination of product function quantity and object from the perspective of big data,as follows:(1)The functional knowledge contained in the patent is extracted.(2)The functional hypergraph is constructed based on the co-occurrence relationship between patents and applicants.(3)The function and patent weight are calculated from the patent applicant’s perspective and patent value.(4)A weight calculation model of the PFC is developed.(5)The weighted frequent subgraph algorithm is used to obtain the optimal function combination list.This method is applied to an innovative design process of a bathroom shower.The results indicate that this method can help frms detach optimal function candidates and develop a multifunctional product.展开更多
This paper discusses the features and relevant theories of GIS spatial data model based on hypergraph,etc.The integrated concept model based on hypergraph and object_oriented model (HOOM) is proposed by the authors.Th...This paper discusses the features and relevant theories of GIS spatial data model based on hypergraph,etc.The integrated concept model based on hypergraph and object_oriented model (HOOM) is proposed by the authors.The principal contribution of this paper is that we study the K_section and other theories of hypergraph.An application example using HOOM is given at the end of the paper.展开更多
To overcome the limitation of the traditional clustering algorithms which fail to produce meaningful clusters in high-dimensional, sparseness and binary value data sets, a new method based on hypergraph model is propo...To overcome the limitation of the traditional clustering algorithms which fail to produce meaningful clusters in high-dimensional, sparseness and binary value data sets, a new method based on hypergraph model is proposed. The hypergraph model maps the relationship present in the original data in high dimensional space into a hypergraph. A hyperedge represents the similarity of attrlbute-value distribution between two points. A hypergraph partitioning algorithm is used to find a partitioning of the vertices such that the corresponding data items in each partition are highly related and the weight of the hyperedges cut by the partitioning is minimized. The quality of the clustering result can be evaluated by applying the intra-cluster singularity value. Analysis and experimental results have demonstrated that this approach is applicable and effective in wide ranging scheme.展开更多
In order to guarantee the wireless multicast throughput at a minimum cost, we propose a layered hypergraph high-dimension clustering algorithm (LayerHC) considering the channels and statistical locations of mobile mem...In order to guarantee the wireless multicast throughput at a minimum cost, we propose a layered hypergraph high-dimension clustering algorithm (LayerHC) considering the channels and statistical locations of mobile members. The algorithm can achieve a minimum multicast spanning tree to obtain a minimum number of relays and effective cooperative areas with low computational complexity.展开更多
Cloud storage has the characteristics of distributed and virtual, and it makes the ownership rights and management rights of users data separated. The master-slave architecture of cloud storage has a problem of single...Cloud storage has the characteristics of distributed and virtual, and it makes the ownership rights and management rights of users data separated. The master-slave architecture of cloud storage has a problem of single point failure. In this paper, we provide a cloud storage architecture model based on Semantic equivalence. According to semantic matching degree, this architecture divides the nodes into node cluster by creating semantic tree and maintains system routing through semantic hypergraph. Through simulation experiments show that dividing network into semantic can enhance scalability and flexibility of the system, and it can improve the efficiency of network organization and the security of cloud storage system, at the same time, it can also reduce the cloud data storage and the delay of reading time.展开更多
In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs...In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs Combin. 2007].展开更多
The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows：Dv（H）≤min{α≤（H）, p（H）, p（H）, T（H）}; De（H）≤min{v（H）, T...The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows：Dv（H）≤min{α≤（H）, p（H）, p（H）, T（H）}; De（H）≤min{v（H）, T（H）, p（H）}; DT（H） ≤αT（H）; S（H）≤ Dv （H） ＋ α（H）≤n; 2≤ Dv （H） ＋ T（H） ≤n; 2 〈 Dv （H） ＋ v（H）≤n/2 ＋ [n/r]; Dv （H） ＋ p（H） 〈_n;2≤De（H） ＋ Dv（H）≤n/2 ＋ [n/r];α（H） ＋ De（H）≤n;2 ≤ De（H） ＋ v（H）≤2[n/r]; 2 De（H） ＋ p（H）≤n-r ＋ 2.展开更多
基金Supported by the Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0884)。
文摘Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.
基金Supported by Natural Science Foundation of HuBei Province(2022CFB299).
文摘This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh principle and the perturbation of the spectral radius under moving the edge operation,and the extremal hypergraphs are characterized for both supertree and unicyclic hypergraphs.The spectral radius of the graph is generalized.
文摘Practical real-world scenarios such as the Internet,social networks,and biological networks present the challenges of data scarcity and complex correlations,which limit the applications of artificial intelligence.The graph structure is a typical tool used to formulate such correlations,it is incapable of modeling highorder correlations among different objects in systems;thus,the graph structure cannot fully convey the intricate correlations among objects.Confronted with the aforementioned two challenges,hypergraph computation models high-order correlations among data,knowledge,and rules through hyperedges and leverages these high-order correlations to enhance the data.Additionally,hypergraph computation achieves collaborative computation using data and high-order correlations,thereby offering greater modeling flexibility.In particular,we introduce three types of hypergraph computation methods:①hypergraph structure modeling,②hypergraph semantic computing,and③efficient hypergraph computing.We then specify how to adopt hypergraph computation in practice by focusing on specific tasks such as three-dimensional(3D)object recognition,revealing that hypergraph computation can reduce the data requirement by 80%while achieving comparable performance or improve the performance by 52%given the same data,compared with a traditional data-based method.A comprehensive overview of the applications of hypergraph computation in diverse domains,such as intelligent medicine and computer vision,is also provided.Finally,we introduce an open-source deep learning library,DeepHypergraph(DHG),which can serve as a tool for the practical usage of hypergraph computation.
基金Project supported by the National Natural Science Foundation of China(Grant No.62166010)the Guangxi Natural Science Foundation(Grant No.2023GXNSFAA026087).
文摘Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important nodes in a directed hypergraph.The algorithm introduces the Jaccard similarity of directed hypergraphs.By comparing the numbers of common neighbors between nodes with the total number of their neighbors,the Jaccard similarity measure takes into account the similarity between nodes that are not directly connected,and can reflect the potential correlation between nodes.An improved susceptible–infected(SI)model in directed hypergraph is proposed,which considers nonlinear propagation mode and more realistic propagation mechanism.In addition,some important node evaluation methods are transferred from undirected hypergraphs and applied to directed hypergraphs.Finally,the ImPageRank algorithm is used to evaluate the performance of the SI model,network robustness and monotonicity.Simulations of real networks demonstrate the excellent performance of the proposed algorithm and provide a powerful framework for identifying important nodes in directed hypergraphs.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12247153,T2293771,and 12247101)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LTGY24A050002)+3 种基金the Sichuan Science and Technology Program(Grant Nos.2024NSFSC1364 and 2023NSFSC1919)the Project of Huzhou Science and Technology Bureau(Grant No.2022YZ29)the UESTCYDRI research start-up(Grant No.U03210066)the New Cornerstone Science Foundation through the Xplorer Prize。
文摘Complex networks play a crucial role in the study of collective behavior,encompassing the analysis of dynamical properties and network topology.In real-world systems,higher-order interactions among multiple entities are widespread and significantly influence collective dynamics.Here,we extend the synchronization alignment function framework to hypergraphs of arbitrary order by leveraging the multi-order Laplacian matrix to encode higher-order interactions.Our findings reveal that the upper bound of synchronous behavior is determined by the maximum eigenvalue of the multi-order Laplacian matrix.Furthermore,we decompose the contribution of each hyperedge to this eigenvalue and utilize it as a basis for designing an eigenvalue-based topology modification algorithm.This algorithm effectively enhances the upper bound of synchronous behavior without altering the total number of higher-order interactions.Our study provides new insights into dynamical optimization and topology tuning in hypergraphs,advancing the understanding of the interplay between higher-order interactions and collective dynamics.
基金Supported by the Key R&D Program of Gansu Province(No.23YFGA0063)the Key Talent Project of Gansu Province(No.2024RCXM57,2024RCXM22)the Major Science and Technology Special Program of Gansu Province(No.25ZYJA037).
文摘Traffic flow prediction is a crucial element of intelligent transportation systems.However,accu-rate traffic flow prediction is quite challenging because of its highly nonlinear,complex,and dynam-ic characteristics.To address the difficulties in simultaneously capturing local and global dynamic spatiotemporal correlations in traffic flow,as well as the high time complexity of existing models,a multi-head flow attention-based local-global dynamic hypergraph convolution(MFA-LGDHC)pre-diction model is proposed.which consists of multi-head flow attention(MHFA)mechanism,graph convolution network(GCN),and local-global dynamic hypergraph convolution(LGHC).MHFA is utilized to extract the time dependency of traffic flow and reduce the time complexity of the model.GCN is employed to catch the spatial dependency of traffic flow.LGHC utilizes down-sampling con-volution and isometric convolution to capture the local and global spatial dependencies of traffic flow.And dynamic hypergraph convolution is used to model the dynamic higher-order relationships of the traffic road network.Experimental results indicate that the MFA-LGDHC model outperforms current popular baseline models and exhibits good prediction performance.
基金Supported by the National Natural Science Foundation of China(Grant No.12371516)the Natural Science Foundation of Liaoning Province(Grant No.2022-MS-152)the Fundamental Research Funds for the Central Universities(Grant No.DUT22LAB305)。
文摘This paper mainly studies the influence maximization problem of threshold models in hypergraphs,which aims to identify the most influential nodes in hypergraphs.Firstly,we introduce a novel information diffusion rule in hypergraphs based on Threshold Models and conduct the stability analysis.Then we extend the CI-TM algorithm,originally designed for complex networks,to hypergraphs,denoted as the H-CI-TM algorithm.Secondly,we use an iterative approach to get the globally optimal solutions.The analysis reveals that our algorithm ultimately identifies the most influential set of nodes.Based on the numerical simulations,HCI-TM algorithm outperforms several competing algorithms in both synthetic and real-world hypergraphs.Essentially,when provided with the same number of initial seeds,our algorithm can achieve a larger activation size.Our method not only accurately assesses the influence of individual nodes but also identifies a set of nodes with greater impact.Furthermore,our results demonstrate good scalability when handling intricate relationships and large-scale hypergraphs.The outcomes of our research provide substantial support for the applications of the threshold models across diverse fields,including social network analysis and marketing strategies.
基金supported by National Natural Science Foundation of China(No.61806006)Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘The existing multi-view subspace clustering algorithms based on tensor singular value decomposition(t-SVD)predominantly utilize tensor nuclear norm to explore the intra view correlation between views of the same samples,while neglecting the correlation among the samples within different views.Moreover,the tensor nuclear norm is not fully considered as a convex approximation of the tensor rank function.Treating different singular values equally may result in suboptimal tensor representation.A hypergraph regularized multi-view subspace clustering algorithm with dual tensor log-determinant(HRMSC-DTL)was proposed.The algorithm used subspace learning in each view to learn a specific set of affinity matrices,and introduced a non-convex tensor log-determinant function to replace the tensor nuclear norm to better improve global low-rankness.It also introduced hyper-Laplacian regularization to preserve the local geometric structure embedded in the high-dimensional space.Furthermore,it rotated the original tensor and incorporated a dual tensor mechanism to fully exploit the intra view correlation of the original tensor and the inter view correlation of the rotated tensor.At the same time,an alternating direction of multipliers method(ADMM)was also designed to solve non-convex optimization model.Experimental evaluations on seven widely used datasets,along with comparisons to several state-of-the-art algorithms,demonstrated the superiority and effectiveness of the HRMSC-DTL algorithm in terms of clustering performance.
文摘An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.
文摘A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower than that of ECP method in several order of magnitude.
文摘We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G = (V, E), its rupture degree r(G<sup>k</sup>) is defined as r(G<sup>k</sup>) = max{ω(G<sup>k</sup> - X) - |X| - m(G<sup>k</sup> - X): X <span style="white-space:nowrap;">⊂ V(G<sup>k</sup>), ω(G<sup>k</sup> - X) > 1}, where X is a cut set (or destruction strategy) of G<sup>k</sup>, ω(G<sup>k</sup> - X) and m(G<sup>k</sup> - X) denote the number of components and the order of a largest component in G<sup>k</sup> - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.
基金Supported by the National Natural Science Foundation of China(Grant No.11161032)
文摘The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.
基金Supported by National Natural Science Foundation of China(Grant No.51875220)China Fujian Province Social Science Foundation Research Project(Grant No.FJ2021B128).
文摘The product functional confguration(PFC)is typically used by frms to satisfy the individual requirements of customers and is realized based on market analysis.This study aims to help frms analyze functions and realize functional confgurations using patent data.This study frst proposes a patent-data-driven PFC method based on a hypergraph network.It then constructs a weighted network model to optimize the combination of product function quantity and object from the perspective of big data,as follows:(1)The functional knowledge contained in the patent is extracted.(2)The functional hypergraph is constructed based on the co-occurrence relationship between patents and applicants.(3)The function and patent weight are calculated from the patent applicant’s perspective and patent value.(4)A weight calculation model of the PFC is developed.(5)The weighted frequent subgraph algorithm is used to obtain the optimal function combination list.This method is applied to an innovative design process of a bathroom shower.The results indicate that this method can help frms detach optimal function candidates and develop a multifunctional product.
文摘This paper discusses the features and relevant theories of GIS spatial data model based on hypergraph,etc.The integrated concept model based on hypergraph and object_oriented model (HOOM) is proposed by the authors.The principal contribution of this paper is that we study the K_section and other theories of hypergraph.An application example using HOOM is given at the end of the paper.
文摘To overcome the limitation of the traditional clustering algorithms which fail to produce meaningful clusters in high-dimensional, sparseness and binary value data sets, a new method based on hypergraph model is proposed. The hypergraph model maps the relationship present in the original data in high dimensional space into a hypergraph. A hyperedge represents the similarity of attrlbute-value distribution between two points. A hypergraph partitioning algorithm is used to find a partitioning of the vertices such that the corresponding data items in each partition are highly related and the weight of the hyperedges cut by the partitioning is minimized. The quality of the clustering result can be evaluated by applying the intra-cluster singularity value. Analysis and experimental results have demonstrated that this approach is applicable and effective in wide ranging scheme.
基金Acknowledgements This work was supported by Natural Science Foundation of Beijing under Grant No. 4102041.
文摘In order to guarantee the wireless multicast throughput at a minimum cost, we propose a layered hypergraph high-dimension clustering algorithm (LayerHC) considering the channels and statistical locations of mobile members. The algorithm can achieve a minimum multicast spanning tree to obtain a minimum number of relays and effective cooperative areas with low computational complexity.
基金supported in part by the National Science and technology support program of China No. 2014BAH29F05the National High-Tech R&D Program (863 Program) No. 2015AA01A705+3 种基金the National Natural Science Foundation of China under Grant No. 61572072the National Science and Technology Major Project No. 2015ZX03001041the Fundamental Research Funds for the Central Universities No. FRF-TP-14-046A2"Research on the System of Personalized Education using Big Data"
文摘Cloud storage has the characteristics of distributed and virtual, and it makes the ownership rights and management rights of users data separated. The master-slave architecture of cloud storage has a problem of single point failure. In this paper, we provide a cloud storage architecture model based on Semantic equivalence. According to semantic matching degree, this architecture divides the nodes into node cluster by creating semantic tree and maintains system routing through semantic hypergraph. Through simulation experiments show that dividing network into semantic can enhance scalability and flexibility of the system, and it can improve the efficiency of network organization and the security of cloud storage system, at the same time, it can also reduce the cloud data storage and the delay of reading time.
基金Supported by the National Natural Science Foundation of China(Grant No.11601368)
文摘In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs Combin. 2007].
基金Supported by Ningbo Institute of Technology, Zhejiang Univ. Youth Innovation Foundation and Zhejiang Provincial Natural Science Foundation( Y604167).
文摘The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows：Dv（H）≤min{α≤（H）, p（H）, p（H）, T（H）}; De（H）≤min{v（H）, T（H）, p（H）}; DT（H） ≤αT（H）; S（H）≤ Dv （H） ＋ α（H）≤n; 2≤ Dv （H） ＋ T（H） ≤n; 2 〈 Dv （H） ＋ v（H）≤n/2 ＋ [n/r]; Dv （H） ＋ p（H） 〈_n;2≤De（H） ＋ Dv（H）≤n/2 ＋ [n/r];α（H） ＋ De（H）≤n;2 ≤ De（H） ＋ v（H）≤2[n/r]; 2 De（H） ＋ p（H）≤n-r ＋ 2.
