Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challen...Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challenging tasks.The goal of subgraph matching is to find all subgraphs in the data graph that are isomorphic to the query graph.Traditional methods mostly rely on search strategies with high computational complexity and are hard to apply to large-scale real datasets.With the advent of graph neural networks(GNNs),researchers have turned to GNNs to address subgraph matching problems.However,the multi-attributed features on nodes and edges are overlooked during the learning of graphs,which causes inaccurate results in real-world scenarios.To tackle this problem,we propose a novel model called subgraph matching on multi-attributed graph network(SGMAN).SGMAN first utilizes improved line graphs to capture node and edge features.Then,SGMAN integrates GNN and contrastive learning(CL)to derive graph representation embeddings and calculate the matching matrix to represent the matching results.We conduct experiments on public datasets,and the results affirm the superior performance of our model.展开更多
This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, ...This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, an effective way for building and drawing weighted directed graphs is presented, forming a foundation for visual implementation of the algorithm in the graph theory.展开更多
A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH（G）,is referred to as the multiplicity of the eigenval...A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH（G）,is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph G with given order and matching number, we give a formula on ηH（G）, which combines the cases of undirected and oriented unicyclic graphs and also corrects an error in Theorem 4.2 of [Xueliang LI, Guihai YU. The skew-rank of oriented graphs. Sci. Sin. Math., 2015, 45：93-104（in Chinese）]. In addition, we characterize all the n-vertex mixed graphs with nullity n-3, which are determined by the spectrum of their Hermitian-adjacency matrices.展开更多
In a cloud environment,outsourced graph data is widely used in companies,enterprises,medical institutions,and so on.Data owners and users can save costs and improve efficiency by storing large amounts of graph data on...In a cloud environment,outsourced graph data is widely used in companies,enterprises,medical institutions,and so on.Data owners and users can save costs and improve efficiency by storing large amounts of graph data on cloud servers.Servers on cloud platforms usually have some subjective or objective attacks,which make the outsourced graph data in an insecure state.The issue of privacy data protection has become an important obstacle to data sharing and usage.How to query outsourcing graph data safely and effectively has become the focus of research.Adjacency query is a basic and frequently used operation in graph,and it will effectively promote the query range and query ability if multi-keyword fuzzy search can be supported at the same time.This work proposes to protect the privacy information of outsourcing graph data by encryption,mainly studies the problem of multi-keyword fuzzy adjacency query,and puts forward a solution.In our scheme,we use the Bloom filter and encryption mechanism to build a secure index and query token,and adjacency queries are implemented through indexes and query tokens on the cloud server.Our proposed scheme is proved by formal analysis,and the performance and effectiveness of the scheme are illustrated by experimental analysis.The research results of this work will provide solid theoretical and technical support for the further popularization and application of encrypted graph data processing technology.展开更多
The relation is a semantic expression relevant to two named entities in a sentence.Since a sentence usually contains several named entities,it is essential to learn a structured sentence representation that encodes de...The relation is a semantic expression relevant to two named entities in a sentence.Since a sentence usually contains several named entities,it is essential to learn a structured sentence representation that encodes dependency information specific to the two named entities.In related work,graph convolutional neural networks are widely adopted to learn semantic dependencies,where a dependency tree initializes the adjacency matrix.However,this approach has two main issues.First,parsing a sentence heavily relies on external toolkits,which can be errorprone.Second,the dependency tree only encodes the syntactical structure of a sentence,which may not align with the relational semantic expression.In this paper,we propose an automatic graph learningmethod to autonomously learn a sentence’s structural information.Instead of using a fixed adjacency matrix initialized by a dependency tree,we introduce an Adaptive Adjacency Matrix to encode the semantic dependency between tokens.The elements of thismatrix are dynamically learned during the training process and optimized by task-relevant learning objectives,enabling the construction of task-relevant semantic dependencies within a sentence.Our model demonstrates superior performance on the TACRED and SemEval 2010 datasets,surpassing previous works by 1.3%and 0.8%,respectively.These experimental results show that our model excels in the relation extraction task,outperforming prior models.展开更多
In this paper,we propose a novel graph signal processing convolution recurrent network(GSP CRN)for signal enhancement against high suppressive interference(HSI)in wireless communications.GSPCRN consists of the short-t...In this paper,we propose a novel graph signal processing convolution recurrent network(GSP CRN)for signal enhancement against high suppressive interference(HSI)in wireless communications.GSPCRN consists of the short-time graph signal processing(SGSP)approach and a modified convolution recurrent network.Similar to the traditional shorttime time-frequency transformation,SGSP frames the complex-valued communication signal and transforms it to the graph-domain representations,where the connection and weight flexibility of each vertex are fully taken into account.In the presence of HSI,SGSP can extract signal features from new graph-domain dimensions and empower neural networks for weak signal enhancement.Two SGSP methods,adjacency singular value decomposition and implicit graph transformation,are designed to capture relationships among the sampling points in the segmented signals.Simulation results demonstrate that our proposed GSPCRN outperforms existing classic methods in extracting weak signals from the HSI environment.When the interference-to-signal ratio exceeds 27dB,only our proposed GSPCRN can achieve the interference mitigation.展开更多
A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism a...A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism are different from its rigid counterparts, so does the structural synthesis method. In order to carry out its structural synthesis, a constraint graph representation for topological structure of compliant metamorphic mechanisms is introduced, which can not only represent the structure of a compliant metamorphic mechanism, but also describe the characteristics of its links and kinematic pairs. An adjacency matrix representation of the link relationships in a compliant metamorphic mechanism is presented according to the constraint graph. Then, a method for structural synthesis of compliant metamorphic mechanisms is proposed based on the adjacency matrix operations. The operation rules and the operation procedures of adjacency matrices are described through synthesis of the initial configurations composed of s＋1 links from an s-link mechanism （the final configuration）. The method is demonstrated by synthesizing all the possible four-link compliant metamorphic mechanisms that can transform into a three-link mechanism through combining two of its links. Sixty-five adjacency matrices are obtained in the synthesis, each of which corresponds to a compliant metamorphic mechanism having four links. Therefore, the effectiveness of the method is validated by a specific compliant metamorphic mechanism corresponding to one of the sixty-five adjacency matrices. The structural synthesis method is put into practice as a fully compliant metamorphic hand is presented based on the synthesis results. The synthesis method has the advantages of simple operation rules, clear geometric meanings, ease of programming with matrix operation, and provides an effective method for structural synthesis of compliant metamorphic mechanisms and can be used in the design of new compliant metamorphic mechanisms.展开更多
Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), i...Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.展开更多
Let G be a simple graph with no isolated edge. An Ⅰ-total coloring of a graph G is a mapping φ : V(G) ∪ E(G) → {1, 2, · · ·, k} such that no adjacent vertices receive the same color and no adjacent ...Let G be a simple graph with no isolated edge. An Ⅰ-total coloring of a graph G is a mapping φ : V(G) ∪ E(G) → {1, 2, · · ·, k} such that no adjacent vertices receive the same color and no adjacent edges receive the same color. An Ⅰ-total coloring of a graph G is said to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, we have C_φ(u) = C_φ(v), where C_φ(u) denotes the set of colors of u and its incident edges. The minimum number of colors required for an adjacent vertex distinguishing Ⅰ-total coloring of G is called the adjacent vertex distinguishing Ⅰ-total chromatic number, denoted by χ_at^i(G).In this paper, we characterize the adjacent vertex distinguishing Ⅰ-total chromatic number of outerplanar graphs.展开更多
In this paper we investigate the least eigenvalue of a graph whose complement is connected,and present a lower bound for the least eigenvalue of such graph.We also characterize the unique graph whose least eigenvalue ...In this paper we investigate the least eigenvalue of a graph whose complement is connected,and present a lower bound for the least eigenvalue of such graph.We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.展开更多
文摘Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challenging tasks.The goal of subgraph matching is to find all subgraphs in the data graph that are isomorphic to the query graph.Traditional methods mostly rely on search strategies with high computational complexity and are hard to apply to large-scale real datasets.With the advent of graph neural networks(GNNs),researchers have turned to GNNs to address subgraph matching problems.However,the multi-attributed features on nodes and edges are overlooked during the learning of graphs,which causes inaccurate results in real-world scenarios.To tackle this problem,we propose a novel model called subgraph matching on multi-attributed graph network(SGMAN).SGMAN first utilizes improved line graphs to capture node and edge features.Then,SGMAN integrates GNN and contrastive learning(CL)to derive graph representation embeddings and calculate the matching matrix to represent the matching results.We conduct experiments on public datasets,and the results affirm the superior performance of our model.
基金Project supported by Science Foundation of Shanghai MunicipalConmission of Education (Grant No .03A203)
文摘This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, an effective way for building and drawing weighted directed graphs is presented, forming a foundation for visual implementation of the algorithm in the graph theory.
基金Supported by the National Natural Science Foundation of China(Grant No.11571360)
文摘A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH（G）,is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph G with given order and matching number, we give a formula on ηH（G）, which combines the cases of undirected and oriented unicyclic graphs and also corrects an error in Theorem 4.2 of [Xueliang LI, Guihai YU. The skew-rank of oriented graphs. Sci. Sin. Math., 2015, 45：93-104（in Chinese）]. In addition, we characterize all the n-vertex mixed graphs with nullity n-3, which are determined by the spectrum of their Hermitian-adjacency matrices.
基金This research was supported in part by the Nature Science Foundation of China(Nos.62262033,61962029,61762055,62062045 and 62362042)the Jiangxi Provincial Natural Science Foundation of China(Nos.20224BAB202012,20202ACBL202005 and 20202BAB212006)+3 种基金the Science and Technology Research Project of Jiangxi Education Department(Nos.GJJ211815,GJJ2201914 and GJJ201832)the Hubei Natural Science Foundation Innovation and Development Joint Fund Project(No.2022CFD101)Xiangyang High-Tech Key Science and Technology Plan Project(No.2022ABH006848)Hubei Superior and Distinctive Discipline Group of“New Energy Vehicle and Smart Transportation”,the Project of Zhejiang Institute of Mechanical&Electrical Engineering,and the Jiangxi Provincial Social Science Foundation of China(No.23GL52D).
文摘In a cloud environment,outsourced graph data is widely used in companies,enterprises,medical institutions,and so on.Data owners and users can save costs and improve efficiency by storing large amounts of graph data on cloud servers.Servers on cloud platforms usually have some subjective or objective attacks,which make the outsourced graph data in an insecure state.The issue of privacy data protection has become an important obstacle to data sharing and usage.How to query outsourcing graph data safely and effectively has become the focus of research.Adjacency query is a basic and frequently used operation in graph,and it will effectively promote the query range and query ability if multi-keyword fuzzy search can be supported at the same time.This work proposes to protect the privacy information of outsourcing graph data by encryption,mainly studies the problem of multi-keyword fuzzy adjacency query,and puts forward a solution.In our scheme,we use the Bloom filter and encryption mechanism to build a secure index and query token,and adjacency queries are implemented through indexes and query tokens on the cloud server.Our proposed scheme is proved by formal analysis,and the performance and effectiveness of the scheme are illustrated by experimental analysis.The research results of this work will provide solid theoretical and technical support for the further popularization and application of encrypted graph data processing technology.
基金supported by the Technology Projects of Guizhou Province under Grant[2024]003National Natural Science Foundation of China(GrantNos.62166007,62066008,62066007)Guizhou Provincial Science and Technology Projects under Grant No.ZK[2023]300.
文摘The relation is a semantic expression relevant to two named entities in a sentence.Since a sentence usually contains several named entities,it is essential to learn a structured sentence representation that encodes dependency information specific to the two named entities.In related work,graph convolutional neural networks are widely adopted to learn semantic dependencies,where a dependency tree initializes the adjacency matrix.However,this approach has two main issues.First,parsing a sentence heavily relies on external toolkits,which can be errorprone.Second,the dependency tree only encodes the syntactical structure of a sentence,which may not align with the relational semantic expression.In this paper,we propose an automatic graph learningmethod to autonomously learn a sentence’s structural information.Instead of using a fixed adjacency matrix initialized by a dependency tree,we introduce an Adaptive Adjacency Matrix to encode the semantic dependency between tokens.The elements of thismatrix are dynamically learned during the training process and optimized by task-relevant learning objectives,enabling the construction of task-relevant semantic dependencies within a sentence.Our model demonstrates superior performance on the TACRED and SemEval 2010 datasets,surpassing previous works by 1.3%and 0.8%,respectively.These experimental results show that our model excels in the relation extraction task,outperforming prior models.
基金supported by he National Social Science Found of China(2022-SKJJ-B-112).
文摘In this paper,we propose a novel graph signal processing convolution recurrent network(GSP CRN)for signal enhancement against high suppressive interference(HSI)in wireless communications.GSPCRN consists of the short-time graph signal processing(SGSP)approach and a modified convolution recurrent network.Similar to the traditional shorttime time-frequency transformation,SGSP frames the complex-valued communication signal and transforms it to the graph-domain representations,where the connection and weight flexibility of each vertex are fully taken into account.In the presence of HSI,SGSP can extract signal features from new graph-domain dimensions and empower neural networks for weak signal enhancement.Two SGSP methods,adjacency singular value decomposition and implicit graph transformation,are designed to capture relationships among the sampling points in the segmented signals.Simulation results demonstrate that our proposed GSPCRN outperforms existing classic methods in extracting weak signals from the HSI environment.When the interference-to-signal ratio exceeds 27dB,only our proposed GSPCRN can achieve the interference mitigation.
基金supported by National Natural Science Foundation of China (Grant No. 51075039, Grant No. 50805110,Grant No. 50705010)Beijing Municipal Natural Science Foundation of China (Grant No. 3082014)the Fundamental Research Funds for the Central Universities of China (Grant No. 2009CZ08, Grant No. JY10000904010)
文摘A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism are different from its rigid counterparts, so does the structural synthesis method. In order to carry out its structural synthesis, a constraint graph representation for topological structure of compliant metamorphic mechanisms is introduced, which can not only represent the structure of a compliant metamorphic mechanism, but also describe the characteristics of its links and kinematic pairs. An adjacency matrix representation of the link relationships in a compliant metamorphic mechanism is presented according to the constraint graph. Then, a method for structural synthesis of compliant metamorphic mechanisms is proposed based on the adjacency matrix operations. The operation rules and the operation procedures of adjacency matrices are described through synthesis of the initial configurations composed of s＋1 links from an s-link mechanism （the final configuration）. The method is demonstrated by synthesizing all the possible four-link compliant metamorphic mechanisms that can transform into a three-link mechanism through combining two of its links. Sixty-five adjacency matrices are obtained in the synthesis, each of which corresponds to a compliant metamorphic mechanism having four links. Therefore, the effectiveness of the method is validated by a specific compliant metamorphic mechanism corresponding to one of the sixty-five adjacency matrices. The structural synthesis method is put into practice as a fully compliant metamorphic hand is presented based on the synthesis results. The synthesis method has the advantages of simple operation rules, clear geometric meanings, ease of programming with matrix operation, and provides an effective method for structural synthesis of compliant metamorphic mechanisms and can be used in the design of new compliant metamorphic mechanisms.
基金Supported by the NNSF of China(10771091)Supported by the Qinglan Project of Lianyungang Teacher’s College(2009QLD3)
文摘Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.
基金Supported by the National Natural Science Foundation of China(61163037,61163054,61363060)
文摘Let G be a simple graph with no isolated edge. An Ⅰ-total coloring of a graph G is a mapping φ : V(G) ∪ E(G) → {1, 2, · · ·, k} such that no adjacent vertices receive the same color and no adjacent edges receive the same color. An Ⅰ-total coloring of a graph G is said to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, we have C_φ(u) = C_φ(v), where C_φ(u) denotes the set of colors of u and its incident edges. The minimum number of colors required for an adjacent vertex distinguishing Ⅰ-total coloring of G is called the adjacent vertex distinguishing Ⅰ-total chromatic number, denoted by χ_at^i(G).In this paper, we characterize the adjacent vertex distinguishing Ⅰ-total chromatic number of outerplanar graphs.
基金Supported by National Natural Science Foundation of China(Grant No.11071002)Program for New Century Excellent Talents in University,Key Project of Chinese Ministry of Education(Grant No.210091)+8 种基金Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103401110002)Science and Technological Fund of Anhui Province for Outstanding Youth(Grant No.10040606Y33)the Natural Science Foundation of Department of Education of Anhui Province(Grant Nos.KJ2011A195KJ2010B136)Project of Anhui Province for Excellent Young Talents in Universities(Grant No.2009SQRZ017ZD)Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University(Grant No.KJJQ1001)Project for Academic Innovation Team of Anhui University(Grant No.KJTD001B)Fund for Youth Scientific Research of Anhui University(Grant No.KJQN1003)Innovation Fund for Graduates of Anhui University
文摘In this paper we investigate the least eigenvalue of a graph whose complement is connected,and present a lower bound for the least eigenvalue of such graph.We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.
