A hypergraph visualization method oriented to hypergraph hyperedges and nodes

Abstract

The application provides a hypergraph visualization method for hypergraph hyperedges and nodes, defines personnel as hypergraph nodes, defines an organization as a hyperedge, calculates topological structure characteristics of the hypergraph according to a hypergraph definition, maps the hyperedge into an ellipse in a drawing space by using an ellipse geometry-based hyperedge visualization algorithm according to the hypergraph definition, determines position parameters of the ellipse, and determines coordinate positions of the nodes in the drawing space by using a hyperedge ellipse constraint-based torus partition node sampling algorithm according to the hypergraph definition and hyperedge ellipse constraint conditions, that is, an association relationship between the personnel and the organization, and visualizes and displays. The visualization result is clear and intuitive, and the overall result is convenient for observation and analysis.

Description

Technical Field

[0001] This invention relates to the field of computer applications, and more specifically to a hypergraph visualization method oriented towards hypergraphs, hyperedges, and nodes. Background Technology

[0002] A hypergraph, also known as a hypernetwork, is an extension and generalization of a regular graph. In a regular graph, an edge represents a relationship between only two nodes. In a hypergraph, however, an edge can contain any number of nodes that share a common relationship; this special type of edge is called a hyperedge.

[0003] Definition of a hypergraph: Assume a finite set of nodes V = {v1, v2, v3, ..., v...} n There exists a set of hyperedges E such that E i ≠Φ(i=1,2...,m) and A binary relation H = (V, E) is called a hypergraph, where V is called a node or vertex of the hypergraph, and E is called a hyperedge. The degree of a node in a hypergraph is defined as the number of hyperedges associated with that node, and the degree of a hyperedge is defined as the number of nodes contained within that hyperedge.

[0004] Because the theory of hypergraphs is more complex and abstract than that of ordinary graphs, hypergraphs can be used to represent the structural relationships within complex network data. However, since the representation of hypergraphs is relatively abstract, a hypergraph visualization algorithm is needed to transform the logical relationships between data into positional relationships in a drawing space in order to facilitate an intuitive understanding of the inherent relationships between data.

[0005] Currently, there is relatively little research on hypergraph visualization. Most existing work focuses on the visualization of hypergraph hyperedges, that is, given the spatial location information of hypergraph nodes, a visualization algorithm is used to find a graph in the drawing space that can cover all nodes in the hyperedge and use it as the hyperedge. This type of method has the following two drawbacks: (1) It requires the spatial location of the hypergraph nodes to be known in advance. (2) The hyperedges and nodes are distributed randomly and irregularly in space. Summary of the Invention

[0006] The purpose of this invention is to propose a hypergraph visualization method oriented towards hypergraph hyperedges and nodes.

[0007] The technical solution to achieve the purpose of this invention is as follows: a hypergraph visualization method oriented towards hypergraphs, hyperedges, and nodes, which uses hypergraph networks to divide people and organizations in the network space into communities, analyzes and mines the relationships between people and organizations, and visualizes them. The steps are as follows:

[0008] Step 1: Define personnel as hypergraph nodes and organizations as hyperedges. Based on the definition of hypergraph, calculate the topological features of the hypergraph.

[0009] Step 2: Based on the definition of a hypergraph, use an elliptical geometry-based hyperedge visualization algorithm to map the hyperedge to an ellipse in the drawing space and determine the position parameters of the ellipse.

[0010] Step 3: Based on the definition of the hypergraph and the hyperedge ellipse constraint, use the annular partition node sampling algorithm based on the hyperedge ellipse constraint to determine the coordinate position of the node in the drawing space, that is, the relationship between personnel and organizations, and display it visually.

[0011] Further, in step 1, the topological features of the hypergraph are calculated according to the definition of a hypergraph, including the degree of nodes, the degree of hyperedges, and the incidence matrix. The specific method is as follows:

[0012] Node superdegree: Define a hypergraph node v i and super-edge E j If v exists i ∈E j Then node v is called i With super-edge E j Related, node v i The degree of a node is defined as the degree of its node v. i The number of associated hyperedges is denoted as d. H (v i ), where v i Let E be the i-th node in the hypergraph. j Let d represent the j-th hyperedge in the hypergraph. H (v i ) represents node v in hypergraph H i The salvation;

[0013] The degree of a hyperedge: the number of nodes contained in the hyperedge, denoted as d. s (E j ), where d s (E j ) indicates that in the hypergraph H, the hyperedge E is... j The number of nodes included, where the index s is related to the node's degree d. H (v i Forming distinctions;

[0014] Incidence matrix: In the incidence matrix B(H) of the hypergraph H=(V,E), each column is a hyperedge E j (j = 1, 2, ..., m), each row is a node v i (i = 1, 2, ..., n), if a node is associated with a hyperedge, the corresponding value in the matrix is ​​1; otherwise, the corresponding value in the matrix is ​​0. This matrix uses 0 and 1 to determine whether a hyperedge contains a certain node. Each element of the matrix is ​​defined as:

[0015]

[0016] Further, in step 2, based on the definition of a hypergraph, an elliptical geometry-based hyperedge visualization algorithm is used to map the hyperedge to an ellipse in the drawing space, determining the position parameters of the ellipse. The specific method is as follows:

[0017] Step 2.1: Define the drawing space;

[0018] Using a two-dimensional coordinate system with x and y axes as the standard coordinate system for the drawing space, the range of the x-axis coordinate is defined as x∈[x0-λ]. x ,x0+λ x The vertical axis coordinate y ranges from y∈[y0-λ]. y ,y0+λ y The drawing space is a space centered at the coordinate point (x0, y0) and of size 2λ. x ×2λ y A rectangle, where λ x and λ y The values ​​are greater than 0, and the x and y coordinate ranges are defined respectively. The x and y values ​​in the table below are only for differentiation and have no practical meaning. (x0, y0) are the coordinates of the center point in the drawing space. The subscripts are only for identification and have no practical meaning.

[0019] Step 2.2: Determine the position of the ellipse corresponding to each hyperedge in the hypergraph in the drawing space;

[0020] Each hyperedge has a unique corresponding ellipse in the drawing space, and each ellipse is uniformly distributed in the drawing space. Assuming that each ellipse rotates around the coordinate point (x0, y0) as its center, the rotation angle is uniformly distributed in the drawing space, and the calculation formula is as follows:

[0021]

[0022] Where, θ j Let E represent the ellipse rotation angle corresponding to the j-th hyperedge;

[0023] Based on this, the ellipse position parameters corresponding to the hyperedge in the drawing space are obtained. Where j corresponds to the index of the hyperedge, a j Let b represent the major axis of the ellipse corresponding to the j-th hyperedge. j Let represent the minor axis of the ellipse corresponding to the j-th hyperedge.

[0024] Furthermore, in step 3, based on the hypergraph definition and the hyperedge ellipse constraint, the annular partition node sampling algorithm based on the hyperedge ellipse constraint is used to determine the coordinate positions of the nodes in the drawing space. The specific method is as follows:

[0025] Step 3.1: Determine the elliptical space constraints of the hypergraph nodes;

[0026] For any hypergraph node v i coordinates (x′) i ,y′ i ) and any hyperedge E j Elliptical position parameter set Based on the hypergraph's incidence matrix B(H), the elliptic space constraints of the hypergraph nodes are:

[0027]

[0028]

[0029] Where i represents the node index, j represents the hyperedge index, and d ij Represents node v i With super-edge E j The position and distance information of the corresponding ellipse, s ij Represents node v i and super-edge E j Based on the constraints, each hypergraph node obtains its corresponding inequality constraint relationship for different hyperedges;

[0030] Step 3.2: Sampling the spatial location of hypergraph nodes;

[0031] First, sort all nodes in the hypergraph in descending order of node extent and remove duplicates to obtain the node extent set, denoted as d. h ={d k h |1≤k≤K}, K is a set d h The size, where the superscript h indicates that it is the set of node superdegrees d H A subset of;

[0032] Secondly, based on the node superdegree set d h The drawing space is divided into annular regions centered at coordinates (x0, y0). Each annular region corresponds to a superdegree in the node superdegree set. The annular region corresponds to the superdegree of a node with a larger superdegree and the annular region corresponds to the superdegree of a node with a smaller superdegree. The method for calculating the annular region is as follows:

[0033]

[0034]

[0035] Where k represents the index of the annular region, R k Let r be the outer diameter of the ring. k R is the inner diameter of the ring. max This represents the maximum value of the outer diameter of the annulus within the drawing space;

[0036] Finally, for each node in the hypergraph, uniform sampling is performed within the corresponding annular region based on its degree. Since the sampling region of a node is an annular region, polar coordinates are used to represent the spatial position of the node.

[0037] For any node v i The method for calculating the polar coordinates of a node with (x0, y0) as its pole is as follows:

[0038]

[0039] ρ i ~Uniform[r k ,R k (9)

[0040] α i ~Uniform[0,2π] (10) Where Uniform represents a uniform distribution, ρ i and α i Representing node v i The polar radius and polar angle;

[0041] node v i The x and y coordinates are calculated as follows:

[0042] x i =x0+ρ i ×cos(α i (11)

[0043] y i =y0+ρ×sin(α) i (12)

[0044] At this point, the spatial location of the nodes in the hypergraph is determined, and the visualization algorithm for the hyperedges and nodes in the hypergraph is completed.

[0045] A hypergraph visualization method oriented towards hypergraphs, hyperedges, and nodes is provided, which realizes hypergraph visualization based on the aforementioned hypergraph, hyperedge, and node-oriented hypergraph visualization method.

[0046] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs hypergraph visualization based on the aforementioned hypergraph visualization method for hypergraphs, hyperedges, and nodes.

[0047] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements hypergraph visualization based on the aforementioned hypergraph-oriented hyperedge and node-oriented hypergraph visualization method.

[0048] Compared with the prior art, the present invention has the following significant advantages: (1) Based on the definition of a hypergraph, a hyperedge visualization algorithm based on elliptical geometry is proposed. The hyperedge is mapped to an elliptical equation in the drawing space. The position parameters of the elliptical equation are adjusted by the algorithm to control the regular distribution of the ellipse in space, thereby realizing the visualization of the hyperedge. (2) Based on the definition of a hypergraph, a circular partition node sampling algorithm based on hyperedge elliptical constraints is proposed. According to the node hyperdegree, the nodes are divided into regions for sampling according to the circular region. Nodes with high hyperdegree tend to be distributed in the center of the space, while nodes with low hyperdegree are scattered around. At the same time, the nodes are constrained by the position conditions of the hyperedge ellipse. The nodes will only be evenly distributed within the space of their own hyperedge and will not overlap with other hyperedges. The visualization results are clear and intuitive, and the overall results are easy to observe and analyze. Attached Figure Description

[0049] Figure 1 This is a flowchart of the hypergraph node sampling process;

[0050] Figure 2 This is a logical structure diagram of a hypergraph embodiment;

[0051] Figure 3 This is a visualization result of HyperGraph. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0053] A hypergraph visualization method oriented towards hypergraphs, hyperedges, and nodes is proposed. This method uses hypergraph networks to divide people and organizations in the network space into communities, and then visualizes the relationships between people and organizations.

[0054] Based on the hypergraph's logical structure, an elliptical geometry-based hyperedge visualization algorithm is used to determine the hyperedge's position in the drawing space. Simultaneously, a circular partition node sampling algorithm based on hyperedge elliptical constraints is used to determine the node's coordinate position in the drawing space. The specific steps include:

[0055] Step 1: In the hypergraph network, define people as hypergraph nodes and organizations as hyperedges. Each organization may contain multiple people, and each person may belong to multiple organizations. Calculate the topological features of the hypergraph based on its definition. The calculated topological features include the degree of nodes, the degree of hyperedges, and the association matrix. The topological features of the hypergraph imply the logical structural relationships within the hypergraph and form the basis for subsequent visualization calculations of hyperedges and nodes.

[0056] Node hyperdegree definition: Define a hypergraph node v i and super-edge E j If v exists i ∈E j Then node v is called i With super-edge E j Related. Node v i The degree of a node is defined as the degree of its node v. i The number of associated hyperedges is denoted as d. H (v i ), where v i Let E be the i-th node in the hypergraph. j Let d represent the j-th hyperedge in the hypergraph. H (v i ) represents node v in hypergraph H i The salvation.

[0057] Hyperedge superdegree definition: The number of nodes contained in a hyperedge, denoted as d. s (E j ), where d s (E j ) indicates that in the hypergraph H, the hyperedge E is... j The number of nodes included, where the index s is related to the node's degree d. H (v i This creates a distinction.

[0058] Definition of incidence matrix: In the incidence matrix B(H) of a hypergraph H = (V, E), each column is a hyperedge E j (j = 1, 2, ..., m), each row is a node v i (i = 1, 2, ..., n), if a node is associated with a hyperedge, the corresponding value in the matrix is ​​1; otherwise, the corresponding value is 0. This matrix uses 0 and 1 to determine whether a hyperedge contains a given node. Each element in the matrix is ​​defined as follows:

[0059]

[0060] Step 2: Hyperedge Visualization Calculation. This invention proposes a hyperedge visualization algorithm based on elliptic geometry, mapping each hyperedge in the hypergraph to an ellipse equation. A typical ellipse equation is defined as:

[0061]

[0062] Where (x0, y0) are the center coordinates of the ellipse equation, θ is the rotation angle of the ellipse about the horizontal axis, and a and b represent the lengths of the major and minor axes of the ellipse, respectively. The algorithm determines the parameters of the ellipse equation corresponding to the hyperedges based on the topological characteristics of the hypergraph, ensuring that the nodes corresponding to the intersection relationships between ellipses coincide. Furthermore, for ease of observation and analysis, the ellipses corresponding to the hyperedges are evenly distributed in the drawing space. The specific calculation steps of the algorithm are as follows:

[0063] Step 2.1: Define the drawing space.

[0064] Using a two-dimensional coordinate system with x and y axes as the standard coordinate system for the drawing space, the range of the x-axis coordinate is defined as x∈[x0-λ]. x ,x0+λ x The vertical axis coordinate y ranges from y∈[y0-λ]. y ,y0+λ y The drawing space is a space centered at the coordinate point (x0, y0) and of size 2λ. x ×2λ y A rectangle, where λ x and λ y The values ​​are greater than 0, and the x and y coordinate ranges are defined respectively. The x and y values ​​in the table below are only for differentiation and have no practical meaning. (x0, y0) are the coordinates of the center point in the drawing space. The subscripts are only for identification and have no practical meaning. They are not related to the subsequent representation of this scheme.

[0065] Step 2.2: Determine the position of the ellipse corresponding to each hyperedge in the hypergraph in the drawing space.

[0066] Each hyperedge has a unique corresponding ellipse in the drawing space, and these ellipses are uniformly distributed in the drawing space. Assume each ellipse is rotated around its center (x0, y0). The rotation angle is uniformly distributed in the drawing space. The formula for calculating the rotation angle of the ellipse corresponding to the j-th hyperedge relative to the horizontal line is as follows:

[0067]

[0068] Where E represents the set of hyperedges, and the ellipse position parameters corresponding to the j-th hyperedge in the drawing space are calculated accordingly. Where j corresponds to the index of the hyperedge, a j Let b represent the major axis of the ellipse corresponding to the j-th hyperedge. j This represents the minor axis of the ellipse corresponding to the j-th superedge, which is adjusted by the developers based on the specific display effect.

[0069] Step 3: Hypergraph Node Visualization Calculation. Based on the hypergraph definition and the hyperedge ellipse constraints obtained in Step 2, a circular partition node sampling algorithm based on hyperedge ellipse constraints is used to determine the coordinate positions of nodes in the drawing space. The hypergraph node sampling process is as follows: Figure 1 As shown, the specific steps are as follows:

[0070] Step 3.1: Determine the spatial constraints of hypergraph nodes. According to the definition of a hypergraph, hypergraph nodes are constrained by the logical relationships of their hyperedges. Similarly, in the drawing space obtained through mapping, the positional relationships of hypergraph nodes are also constrained by the positions of their hyperedge ellipses. Therefore, before calculating the spatial positions of hypergraph nodes, it is necessary to first determine the spatial constraints of the hyperedge ellipses. For any node v... i coordinates (x) i ,y i ) and any hyperedge E j Elliptical position parameter set Based on the hypergraph's incidence matrix B(H), the formula for calculating the elliptic space constraints of a node is:

[0071]

[0072]

[0073] Where, d ij Represents node v i and super-edge E j The position and distance information of the corresponding ellipse, s ij Represents node v i and super-edge E j The constraints are then defined. Based on this, each hypergraph node obtains its corresponding inequality constraints for different hyperedges.

[0074] Step 3.2: Hypergraph Node Spatial Position Sampling. Based on the obtained node constraint relationships, uniformly distribute and sample the spatial positions of nodes within the drawing space. This invention proposes a node sampling algorithm based on circular partitioning, which satisfies the condition that nodes with large superdegrees tend to be distributed in the center of the drawing space, while nodes with small superdegrees tend to be distributed on the outer side of the space, making the sampled hypergraph node spatial positions clearer and more intuitive. The specific calculation steps are as follows:

[0075] (1) First, sort all nodes in the hypergraph in descending order of node extensibility and remove duplicates to obtain the node extensibility set, denoted as d. h ={d k h |1≤k≤K}, K is a set d h The size, where the superscript h indicates that it is the set of node superdegrees d H A subset of.

[0076] (2) Secondly, based on the node superdegree set d h The drawing space is divided into annular regions centered at coordinates (x0, y0). Each annular region corresponds to a superdegree in the node superdegree set. The annular region with a larger superdegree is in the inner circle, and the annular region with a smaller superdegree is in the outer circle. The method for calculating the annular region is as follows:

[0077]

[0078]

[0079] Where k represents the index of the annular region, R k Let r be the outer diameter of the ring. k R is the inner diameter of the ring. max This represents the maximum value of the outer diameter of the annulus within the drawing space.

[0080] (3) Finally, each node in the hypergraph is uniformly sampled within its corresponding annular region based on its hyperdegree. Since the sampling region of a node is an annular region, this invention uses polar coordinates to represent the spatial position of the node. For any node v i The method for calculating the polar coordinates of a node with (x0, y0) as the pole is as follows:

[0081]

[0082] ρ i ~Uniform[r k ,R k (9)

[0083] θ i ~Uniform[0,2π] (10)

[0084] Where Uniform represents a uniform distribution, ρ i and θ i Representing node v respectively i The polar radius and polar angle. Node v i The x and y coordinates are calculated as follows:

[0085] x i =x0+ρ i ×cos(θ) (11)

[0086] y i =y0+ρ×sin(θ) (12)

[0087] At this point, the spatial locations of the nodes in the hypergraph are determined, and the visualization algorithm for hyperedges and nodes in the hypergraph is complete. The spatial locations of hyperedges and nodes obtained by this algorithm are constrained by the drawing space, and subsequent visualization applications can be extended based on this.

[0088] In summary, this invention, based on the hypergraph's logical structure, uses an elliptical geometry-based hyperedge visualization algorithm to determine the positional information of hyperedges in the drawing space, and simultaneously employs a toroidal partitioning node sampling algorithm based on hyperedge elliptical constraints to determine the coordinate positions of nodes in the drawing space. The results obtained by this visualization method not only conform to the logical structure expressed by the hypergraph itself, but also reorganize the positions of hyperedges and nodes, ensuring that hyperedges are regularly distributed in the drawing space, while guaranteeing that nodes are evenly distributed and non-overlapping only within their respective hyperedges. The visualization results are clear and intuitive, facilitating observation and analysis. It maps the logical relationships between people and organizations in cyberspace to the physical location relationships of nodes and hyperedges in the hypergraph space, providing a clear and intuitive analysis of the inherent connections between target personnel and the flow paths of information propagation from a visualization perspective.

[0089] Example

[0090] To verify the effectiveness of the present invention, the following simulation experiment was conducted.

[0091] Input: The input to this solution is the affiliation of individuals and organizations in a cyberspace scenario. Specifically, each individual is considered a node, represented by an ID (e.g., 0, 1, 2, 3, etc.), and organizations are considered a set of nodes containing the IDs of the individuals. A specific implementation example input is as follows:

[0092] The node list of the hypergraph is [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55], and the hyperedge list is [[0,1,2,3,4,5,6,7,8,9,10,16,17,18,32,19,20,21,22,23, [24,25],[6,7,8,9,10,11,12,13,14,15,21,22,23,24,25,26,27,33,28,29,30,31],[16,17,18,32,34,35,36,37,38,39,40,41,42],[21,22,23,24,25,32,19,20,26,27,33,39,40,41,42,43,44,45,46,47,48,49,50],[28,29,30,31,33,47,48,49,50,51,52,53,54,55]]. The logical structure diagram of the hypergraph is as follows. Figure 2 As shown.

[0093] Step 1: Calculate the topological features of the hypergraph. Hypergraph Incidence Matrix:

[0094] {0:[0],1:[0],2:[0],3:[0],4:[0],5:[0],6:[0,1],7:[0,1],8:[0,1],9:[0,1],10:[0,1],11:[1],12:[1],13:[1],14:[1],15:[1],16:[0,2],17:[0,2],18:[0,2],19:[0,3],20:[0,3],21:[0,1,3],22:[0,1,3],23:[0,1,3],24:[0,1,3],25:[0,1,3],26:[1,3],27:[1,3 ],28:[1,4],29:[1,4],30:[1,4],31:[1,4],32:[0,2,3],33:[1,3,4],34:[2],35:[2],36:[2],37:[2],38:[2],39:[2,3],40:[2,3],41:[2,3],42:[2,3],43:[3],44:[3],45:[3],46:[3],47:[3,4],48:[3,4],49:[3,4],50:[3,4],51:[4],52:[4],53:[4],54:[4],55:[4]}

[0095] For ease of calculation and visualization, the association matrix is ​​not stored in traditional matrix form, but rather in JSON format. The keys represent nodes, and the values ​​represent the set of hyperedges. The node hyperdegree statistics of the hypergraph are as follows:

[0096] {1:[0,1,2,3,4,5,11,12,13,14,15,34,35,36,37,38,43,44,45,46,51,52,53,54,55],2:[6,7,8,9,10,16,17,18,19,20,26,27,28,29,30,31,39,40,41,42,47,48,49,50],3:[21,22,23,24,25,32,33]}

[0097] The key represents the degree of a node, and the value represents the set of nodes.

[0098] Step 2: Determine the spatial location parameters of the hypergraph's hyperedge ellipse. The ellipse equation parameters of the hyperedge are:

[0099] {0:[0,0,50,25,0],1:[0,0,50,25,36],2:[0,0,50,25,72],3:[0,0,50,25,108],4:[0,0,50,25,144]}

[0100] Here, the key represents the hyperedge, and the value represents the ellipse position parameters, which respectively represent the x-coordinate of the ellipse center, the y-coordinate, the major axis a, the minor axis b, and the rotation angle θ.

[0101] Step 3: Determine the coordinates of the hypergraph nodes. Node coordinates are:

[0102] {21:(13.990280581265871,-0.501857592400348),22:(-1.9864075328724418,-0.5911692818881561),23:(0.9078776272670149,-14.442551990488623),24:(-4.06282331617718,2.568872233897021),25:(1.6771808227419718,-3.364956520671253),32:(5.459815978228193,-3.057422050866859),33:(4.188054241648924,4.92582285414325),6:(28.972664864769797,13.116570410623874),7:(29.725230998346195,8.650696937293993),8:(29.559111018281346,9.219672886430207),9:(-31.190530236511208,-5.8196502457595525),10:(-29.483653901466816,-11.331989121044591),16:(8.721338505468358,-20.743080827696378),17:(19.510137648690154,7.312670550875862),18:(11.822315052618487,-11.294926594416248),19:(-15.40539723849747,12.104177551888155),20:(20.708446399613212,-19.604915179240482),26:(-11.436023766808825,-14.540524458090742),27:(23.677468400814185,0.12964660424332777),28:(14.369856112140235,-11.6828661833695),29:(-23.96271361408023,2.5617470317021223),30:(3.773604500456083,23.84880019472169),31:(-6.689276177010293,21.301702249559593),39:(-5.119479043600059,-31.387232883903884),40:(-1.2138342829990676,31.4234104975662),41:(-0.8183165797089259,30.592982898412338),42:(1.2957308318423093,31.47400513381221),47:(-19.452703696730424,23.900088666128028),48:(16.64917277490848,-26.700224170728884),49:(15.687018752471081,-26.818075181394136),50:(-16.59670805514777,25.94293721495858),0:(46.90885817858969,3.527557429984538),1:(-43.97291992387053,8.31161642865042),2:(45.90811962283473,-6.537906120733911),3:(-43.06924229825139,-1.7748745106960722),4:(43.36367011819887,-4.190236126727804),5:(43.90836605575621,-1.0401959909116638),11:(27.434025407559417,32.27748152028044),12:(41.09559412541797,17.799029975884135),13:(35.30242370976593,29.389041431958034),14:(29.51043493111189,32.27343948903634),15:(-40.628618364544884,-19.676641672354325),34:(-14.503030645682754,-38.626512211836214),35:(-20.98253714082806,-42.104092648001384),36:(11.633242033459279,44.74157190382357),37:(5.366963140548946,40.73717837275055),38:(-17.371699810417468,-38.383790738882155),43:(-17.985066655898482,41.602366477852456),44:(3.308031524700553,-44.97871386573981),45:(-21.766960298455334,37.83302452881799),46:(22.636452198529845,-39.43130642527086),51:(39.13975 11857706,-26.211324553421285),52:(-27.90135198459058,34.03406583935524),53:(-41.85950614372656,18.097032188913296),54:(-33.06100773816084,28.49830933763661),55:(-35.08236222117608,23.362067455068907)}.

[0103] Here, the key represents a node, and the value represents the horizontal and vertical coordinates.

[0104] Output: After steps 2 and 3, the position information of the hypergraph's hyperedges and nodes is obtained, taking approximately 0.05 seconds. A visualization tool is used to draw the hyperedge ellipses and node coordinates in the drawing space, as shown below. Figure 3 As shown.

[0105] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A hypergraph visualization method oriented towards hypergraph hyperedges and nodes, characterized in that, Using Hypergraph Networks to categorize individuals and organizations in cyberspace into communities, and analyzing, mining, and visualizing the relationships between individuals and organizations, the steps are as follows: Step 1: Define personnel as hypergraph nodes and organizations as hyperedges. Based on the hypergraph definition, calculate the topological features of the hypergraph. The specific method is as follows: Node superdegree: Define a hypergraph node and super edge If it exists Then it is called a node. With super-edge Related, nodes The degree of a node is defined as its degree. The number of associated superedges is denoted as ,in, For the hypergraph 1 node Indicates the first in the hypergraph One super-edge, Hypergraph Middle node The salvation; The degree of a hyperedge: the number of nodes contained in the hyperedge, denoted as . ,in, Indicates in the hypergraph Chinese Super League Number of nodes included, index It is related to node expiration Forming distinctions; Correlation Matrix: Hypergraph Correlation matrix In the middle, each column is a super-edge. Each row is a node. If a node is associated with a hyperedge, the corresponding value in the matrix is ​​1; otherwise, the corresponding value is 0. This matrix uses 0 and 1 to determine whether a hyperedge contains a certain node. Each element of the matrix is ​​defined as follows: (1)； Step 2: Based on the definition of a hypergraph, use an elliptical geometry-based hyperedge visualization algorithm to map the hyperedge to an ellipse in the drawing space and determine the position parameters of the ellipse. The specific method is as follows: Step 2.1: Define the drawing space; Using a two-dimensional coordinate system with x and y axes as the standard coordinate system for the drawing space, define the range of the x-axis coordinates. y-axis range The drawing space is a space defined by coordinate points. Centered on, size is A rectangle, wherein, and The values ​​are greater than 0, defining the x-coordinate range and y-coordinate range respectively. The subscripts x and y are only used for differentiation and have no practical meaning. These are the coordinates of the center point in the drawing space; the subscript is for identification purposes only and has no actual meaning. Step 2.2: Determine the position of the ellipse corresponding to each hyperedge in the hypergraph in the drawing space; Each hyperedge has a unique corresponding ellipse in the drawing space, and each ellipse is uniformly distributed in the drawing space. Let the ellipses be defined by coordinates of points... As the center of the ellipse, around the coordinate point If rotated, the rotation angle is evenly distributed in the drawing space, and the calculation formula is as follows: ， (3)； in, This represents the ellipse rotation angle corresponding to the j-th hyperedge. Denotes the set of superedges; Based on this, the ellipse position parameters corresponding to the hyperedge in the drawing space are obtained. Where j corresponds to the index of the superedge. Let the major axis of the ellipse corresponding to the j-th hyperedge be denoted as . Let represent the minor axis of the ellipse corresponding to the j-th hyperedge; Step 3: Based on the hypergraph definition and hyperedge ellipse constraints, use the annular partitioning node sampling algorithm based on hyperedge ellipse constraints to determine the coordinate positions of nodes in the drawing space, i.e., the relationships between personnel and organizations, and then visualize them. The specific method is as follows: Step 3.1: Determine the elliptical space constraints for the hypergraph nodes; For any hypergraph node coordinates and any hyperedge Elliptical position parameter set Based on the hypergraph's correlation matrix The elliptical space constraints of the hypergraph nodes are: (4)； (5)； Where i represents the index of the node, and j represents the index of the superedge. Represents a node With super-edge The position and distance information of the corresponding ellipse, Represents a node and super edge Based on the constraints, each hypergraph node obtains its corresponding inequality constraint relationship for different hyperedges; Step 3.2: Sampling the spatial location of hypergraph nodes; First, sort all nodes in the hypergraph in descending order of node extent and remove duplicates to obtain the node extent set, denoted as . , , For set Size, superscript It represents the set of node extrema. A subset of; Secondly, based on the node super-degree set The drawing space is arranged in a circle using coordinates. The system divides the region into regions centered on a node. Each annular region corresponds to a superdegree in the node superdegree set. The annular regions are located in the inner circle, and the annular regions are located in the outer circle. The method for calculating the annular regions is as follows: (6)； (7)； in, Indicates the sequence number of the annular region. The outer diameter of the ring. Let be the inner diameter of the ring. This represents the maximum value of the outer diameter of the annulus within the drawing space; Finally, for each node in the hypergraph, uniform sampling is performed within the corresponding annular region based on its degree. Since the sampling region of a node is an annular region, polar coordinates are used to represent the spatial position of the node. For any node ,by The method for calculating the polar coordinates of nodes that are poles is as follows: (8)； (9)； (10)； in, Represents a uniform distribution. and Representing nodes respectively The polar radius and polar angle; node The x and y coordinates are calculated as follows: (11)； (12)； At this point, the spatial location of the nodes in the hypergraph is determined, and the visualization algorithm for the hyperedges and nodes in the hypergraph is completed.

2. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it realizes hypergraph visualization based on the hypergraph visualization method for hypergraphs, hyperedges, and nodes as described in claim 1.

3. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it realizes hypergraph visualization based on the hypergraph visualization method for hypergraphs, hyperedges, and nodes as described in claim 1.

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