A high-influence information disseminator identification method based on circle graph random walk

Abstract

The application relates to the technical field of graph processing, in particular to a high-influence information disseminator identification method based on circle graph random walk. The application can effectively identify high-influence information disseminators by constructing a user relationship network, a circle relationship network, forming a circle graph, and combining with multilayer random walk to calculate node importance scores. The method has the advantages that the user relationship and the circle structure are deeply fused, the node dissemination capacity is analyzed from a multi-dimensional network perspective, compared with a traditional single network model, the complex paths of information dissemination in a social scene and the synergistic effect between nodes can be better captured, and the accuracy and comprehensiveness of high-influence dissemination node identification are improved.

Description

Technical Field

[0001] This invention relates to the field of graph processing technology, specifically a method for identifying high-influence information disseminators based on circular graph random walks. Background Technology

[0002] Identifying high-influence disseminators is a key task in social network analysis. Its goal is to accurately identify the set of high-influence dissemination nodes with strong propagation effectiveness in large-scale networks. As social networks continue to expand and their structures become increasingly complex, efficiently and accurately identifying truly high-influence dissemination nodes with broad propagation potential from a vast and heterogeneous set of nodes has become a significant challenge in current research.

[0003] Current mainstream methods can be divided into three categories:

[0004] 1. Node-centric methods (such as degree centrality and core centrality): These methods measure node importance through local or global topological features, but they struggle to distinguish between higher-order interactions between nodes, easily leading to convergence in node importance scores and the phenomenon of "pseudo-critical node redundancy." For example, degree-centric methods in social networks often cause highly clustered nodes to form "rich people's clubs," resulting in overlapping propagation influence.

[0005] 2. Dynamic propagation models based on random walks (such as PageRank, HITS, etc.): These methods assess the influence of nodes by simulating the information diffusion process, but traditional single-layer random walks are difficult to capture high-order structures in the network, resulting in failure to identify long-range associations and hidden propagation hubs.

[0006] 3. End-to-end models based on machine learning (such as RCNN, MRCNN, etc.): Although these methods can adaptively extract network features, their black-box nature makes it difficult for the model to explicitly model the coupling relationship between low-order structures (direct connections between nodes) and loop structures (multi-node collaboration), and their generalization ability is limited in sparse or dynamic networks.

[0007] The common drawback of the above methods is their failure to systematically integrate the multi-scale structural information of the network. These problems directly lead to bottlenecks in the identification of high-influence information disseminators, such as limited coverage, high redundancy, and insufficient robustness.

[0008] Therefore, there is an urgent need to construct an identification method that can uniformly model multi-type structural dependencies and accurately identify high-influence propagation nodes, so as to improve the accuracy, stability and practical effectiveness of propagator identification in complex networks. Summary of the Invention

[0009] To avoid and overcome the technical problems existing in the prior art, this invention provides a method for identifying high-influence information disseminators based on circular graph random walks. This invention can effectively improve the accuracy of identifying high-influence dissemination nodes.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] A method for identifying high-influence information disseminators based on circular graph random walks includes the following identification steps:

[0012] S1. Obtain the user list and the relationship data between users in the current social scenario, and construct an undirected and unweighted user relationship network with users as the original nodes and the relationships between users as the edges.

[0013] S2. Obtain all basic circles in the user relationship network and map all basic circles to their corresponding circle nodes;

[0014] S3. Use the circle similarity matrix to add edges between circle nodes, and use the circle nodes and the edges to construct a circle relationship network;

[0015] S4. Connect the circle nodes and their respective original nodes through inter-layer edges, and calculate the weight of each inter-layer edge so that the user relationship network and the circle relationship network are connected to each other to form a circle graph.

[0016] S5. Based on the weights of the edges connecting each layer in the circle graph, calculate the importance score of each original node.

[0017] S6. Select the items with the highest importance scores. K A cluster of original nodes constitutes a high-influence information dissemination node cluster.

[0018] As a further aspect of the present invention, the process of constructing the user relationship network is as follows:

[0019] S11. Call the social platform's open interface to obtain the user list and the relationship data between users;

[0020] S12. Perform structured cleaning on the relational data, and build a network model using users as the original nodes and the relationships between users as the original edges to form a user relationship network. .

[0021] As a further aspect of the present invention, the process of obtaining the circle nodes is as follows:

[0022] S21, Selection Using the original node with the highest degree as the root node, an acyclic tree is generated using the breadth-first spanning tree search algorithm. ; Identification All not included The original edges in the tree are identified and marked as non-tree edges; for each non-tree edge, in Find the unique path between its two endpoints, which forms a basic cycle with the non-tree edges; use this to find... All the basic circles in the middle;

[0023] S22. By directly treating the basic circles as a node, all basic circles are mapped to corresponding nodes, which are called circle nodes.

[0024] As a further aspect of the present invention, the construction process of the circle relationship network is as follows:

[0025] S31. Calculate the cyclic adjacency similarity between two cyclic nodes respectively, and establish a cyclic adjacency similarity matrix;

[0026] S32. Negate the cyclic adjacency similarity matrix and use each element in the negative cyclic adjacency similarity matrix as weights to construct a weighted undirected graph consisting of cyclic nodes. Without forming loops, construct a minimum spanning tree connecting all cyclic nodes in the weighted undirected graph, and select the minimum spanning tree with the smallest sum of weights as the cyclic relationship network. .

[0027] As a further aspect of the present invention, the formula for calculating the similarity of cyclic adjacency is as follows:

[0028] ;

[0029] In the formula, Indicates the first Each circle node; Indicates the first Each circle node; express and Cyclic adjacency similarity between them; express The set of edges consisting of all the original edges contained therein. express The set of edges consisting of all the original edges contained therein; express and The number of identical original edges contained within; express and The total number of categories of the original edges included.

[0030] As a further aspect of the present invention, the formula for calculating the weight of inter-layer connections is as follows:

[0031] ;

[0032] In the formula, Indicates the connection of the first Original nodes and The weight of the inter-layer connections; express The number of basic circles involved in their formation; express The corresponding basic circle; express The number of original nodes in the data; express The average number of basic cycles formed by all original nodes in the network.

[0033] As a further aspect of the present invention, the calculation process for the importance score is as follows:

[0034] S51, Formulating and Random walks between layers can be categorized into intra-layer random walks and cross-layer random walks; intra-layer random walks are... or Internally, nodes randomly transfer between each other; cross-layer random walks are divided into... arrive Upward random transfer and from Back The downward random transfer;

[0035] S52, calculated Adjacency transition matrix:

[0036] exist In the middle, assume the random walk is currently located at Then its next step will be to randomly transition to a state with equal transition probability. Neighbor set A certain circle of nodes Calculate the state transition probability and construct a system using the state transition probability as elements. adjacency transition matrix ;

[0037] S53. Similarly, calculate according to the content in step S52. adjacency transition matrix ;

[0038] S54. Construct the adjacency shift matrix for cross-layer uplink random transitions:

[0039] from arrive When performing an upward random transfer, assume the random walk is currently located at... Then its next step will be randomly transferred to the corresponding upward transfer probability. ; Calculate the upward transition probability, and use the upward transition probability as elements to construct the transition from arrive Adjacency Upshift Matrix ;

[0040] S55. Construct the adjacency shift matrix for cross-layer downlink random transitions:

[0041] from arrive When performing a downlink random transfer, assume the random walk is currently at... Then its next step will be randomly transferred to the corresponding downlink transfer probability. ; Calculate the downlink transition probability, and construct a sequence using the downlink transition probability as elements from arrive Adjacency shift matrix ;

[0042] S56. Combining intra-layer and inter-layer random walks to form multi-layer random walks: By fusing the adjacency transition matrix, adjacency upshift matrix, and adjacency downshift matrix, a complete multi-layer random walk transition matrix is ​​obtained: ;

[0043] S57, Set for time middle The access probability vector, then its Access probability vector at time step It is expressed as follows:

[0044] ;

[0045] S58. Determine if convergence has occurred and output the importance scores of the original nodes: If the convergence condition is met... If the condition is met, the iteration terminates; otherwise, the iteration continues. express and The second norm of the difference between them Indicates the convergence threshold;

[0046] The access probability vector of the original node obtained after convergence is used as the importance score of the original node.

[0047] As a further aspect of the present invention, the state transition probability is represented as follows:

[0048] ;

[0049] In the formula, Indicates from Random transfer to The state transition probability; express The set of all edges in the array.

[0050] As a further aspect of the present invention, the uplink transition probability is expressed as follows:

[0051] ;

[0052] In the formula, Indicates from Random transfer to The probability of the uplink transition; This indicates that the connection is made through inter-layer edges. The set of all connected circular nodes; Indicates connection and the Each circle node The weight of the inter-layer connections.

[0053] As a further aspect of the present invention, the downlink transition probability is expressed as follows:

[0054] ;

[0055] In the formula, Indicates from Random transfer to The probability of a downlink transition; Indicates the first One original node; Indicates connection and The weight of the inter-layer connections.

[0056] Compared with the prior art, the beneficial effects of the present invention are:

[0057] 1. This invention effectively identifies high-influence information disseminators by constructing user relationship networks and circle relationship networks to form a circle graph, and combining this with multi-level random walks to calculate node importance scores. Its advantage lies in the deep integration of user relationships and circle structures, analyzing node propagation capabilities from a multi-dimensional network perspective. Compared to traditional single-network models, it better captures the complex paths of information propagation in social scenarios and the synergistic effects between nodes, improving the accuracy and comprehensiveness of identification.

[0058] 2. During the construction of the user relationship network, data was obtained by calling social platform interfaces and then subjected to structured cleaning to ensure the authenticity and standardization of the data. The advantage of this step is that it is based on real social relationships, avoiding data bias and laying a reliable foundation for subsequent circle structure analysis. This allows the constructed network to accurately reflect the actual user interaction relationships, enhancing the practicality and operability of the method.

[0059] 3. The breadth-first spanning tree search algorithm is used to identify basic cycles and map them to cycle nodes. The advantage of this process is that it efficiently and systematically extracts the cycle structure in the network. By combining the spanning tree with non-tree edges, all basic cycles can be found completely and without redundancy, providing accurate basic units for constructing a cycle relationship network, and enabling cycle nodes to truly reflect the cyclic association characteristics in the network topology.

[0060] 4. A circle relationship network is constructed based on the circle adjacency similarity matrix. The similarity between circles is quantified by calculating the intersection and union of edge sets, and a minimum weighted spanning tree connects the circle nodes. Its advantage is that it characterizes the degree of association between circles from the perspective of edge sharing, enabling the circle relationship network to reflect the topological similarity and dependency of the circle structure. It provides a reasonable inter-circle transfer logic for cross-layer random walks and enhances the model's ability to express the network structure.

[0061] 5. The formula for calculating the weight of inter-layer connections comprehensively considers the number of basic circles in which the original node participates, the average number of circles in which nodes within the circle participate, and the number of nodes in the circle. Its advantage is that it quantifies the connection strength between the original node and the circle nodes from multiple dimensions. This weight reflects the depth of a node's participation in the circle structure and the influence of the circle's size, making the calculation of cross-layer transition probabilities more closely match the actual distribution of a node's influence in the network, and providing key weight support for accurately assessing node importance.

[0062] 6. By defining intra-layer and cross-layer random walk methods, a transition matrix is ​​constructed and the access probability is iteratively calculated until convergence. The converged probability is used as the node importance score. Its advantage is that, by leveraging a multi-layer random walk model, it fully considers the interaction between the original node network and the circle node network, dynamically capturing the propagation patterns of information between different network layers. This allows the importance score calculation to comprehensively consider both local network features and global structure, improving the scientific rigor and reliability of high-influence node identification. Attached Figure Description

[0063] Figure 1 This is a flowchart of the present invention.

[0064] Figure 2 This refers to the user relationship network in this invention.

[0065] Figure 3 This refers to the loop relationship network in this invention.

[0066] Figure 4 This is a circle diagram in the present invention. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] Please see Figure 1 In this embodiment of the invention, a method for identifying high-influence information disseminators based on circular graph random walks includes the following:

[0069] I. Building a User Relationship Network

[0070] Obtain the user list and relationship data within the current social context, and construct an undirected, unweighted user relationship network with users as the original nodes and the relationships between users as the edges; the specific steps are as follows:

[0071] S11. Call the social platform's open interface to obtain user attribute data (user ID, registration time, geographical location) and explicit social relationship data (following / follower list, friend relationship chain).

[0072] S12. Perform structured cleaning on the collected raw data (such as removing duplicates, correcting errors, and filling missing values), abstract users as nodes, and abstract the relationships between users as edges to form a network model, thus forming a user relationship network. And it serves as the input layer. The original node used in this embodiment is... , constitute like Figure 2 As shown.

[0073] II. Obtaining Cyclic Nodes

[0074] Obtain all basic circles in the user relationship network and map each basic circle to its corresponding circle node; the specific steps are as follows:

[0075] S21, Selection Using the original node with the highest degree as the root node, an acyclic tree is generated using the breadth-first spanning tree search algorithm. ; Identification All not included The original edges in the tree are identified and marked as non-tree edges; for each non-tree edge, in Find the unique path between its two endpoints, which forms a basic cycle with the non-tree edges; use this to find... All the basic circles in the equation. The basic circles that make up the equation are as follows: Figure 3 As shown, they are respectively .

[0076] S22. By directly treating the basic circles as a node, all basic circles are mapped to corresponding nodes, which are called circle nodes.

[0077] Will Each basic cycle in the graph is mapped to a new node; Mapped to circle nodes , Mapped to circle nodes , Mapped to circle nodes , Mapped to circle nodes , Mapped to circle nodes , specifically Figure 3 As shown.

[0078] III. Building a Network of Circle Relationships

[0079] We use a cycle similarity matrix to add edges between cycle nodes, and then construct a cycle relationship network using the cycle nodes and these edges; the specific steps are as follows:

[0080] S31. Calculate the cyclic adjacency similarity between two cyclic nodes respectively, and establish a cyclic adjacency similarity matrix. The formula for calculating the similarity of circular adjacencies is as follows:

[0081] ;

[0082] The cyclic adjacency similarity matrix is ​​represented as follows, with the cyclic nodes in each row ordered as follows: :

[0083] ;

[0084] S32. Negate the cyclic adjacency similarity matrix and use each element in the negative cyclic adjacency similarity matrix as weights to construct a weighted undirected graph consisting of cyclic nodes. Without forming loops, construct a minimum spanning tree connecting all cyclic nodes in the weighted undirected graph, and select the minimum spanning tree with the smallest sum of weights as the cyclic relationship network. The details are as follows:

[0085] Construct a maximum spanning tree as the backbone connection, and apply it to the cyclic adjacency similarity matrix. Perform the negative operation: The purpose of this operation is to transform the matrix from one where "the larger the element value, the higher the similarity" to one where "the smaller the element value, the lower the connection cost", thus meeting the requirements of the minimum spanning tree algorithm for setting edge weights.

[0086] Subsequently in the matrix The minimum spanning tree algorithm is applied to the corresponding weighted undirected graph. Its core idea is: in a weighted undirected graph, select a set of edges that connect all nodes without forming cycles, and minimize the sum of the weights of all selected edges. Since the edge weights here come from... This is the negative value of similarity. Therefore, the algorithm is equivalent to maximizing the overall adjacency similarity of the basic cycles in the graph. In other words, the minimum spanning tree algorithm can prioritize retaining the edges with the strongest structural similarity among all possible cycle pair connections, remove redundant connections, and extract the highly correlated skeleton.

[0087] Finally, edges from this minimum spanning tree are added to cyclic nodes as their basic connection structure, thereby constructing a cyclic relationship network characterized by high cyclic adjacency similarity while ensuring connectivity. And it serves as the presentation layer.

[0088] IV. Constructing a Circle Graph

[0089] By connecting the cycle nodes to their respective original nodes through inter-layer edges and calculating the weights of each inter-layer edge, the user relationship network and the cycle relationship network are connected to form a cycle graph; the specific steps are as follows:

[0090] S41, Establish and The interlayer connections between layers, as mentioned in step S22, Mapped to circle nodes , Mapped to circle nodes , Mapped to circle nodes , Mapped to circle nodes , Mapped to circle nodes Therefore, In respectively with In The nodes are connected, and the connections between the remaining nodes and the original nodes are similar, thus forming... and Interlayer connections between layers. Completed loop diagram. like Figure 4 As shown, the inter-layer connections are formed by the input layer. and presentation layer The dashed lines connecting them indicate that they are connected.

[0091] S42. Add weights to the inter-layer connections, calculated according to the formula below:

[0092] ;

[0093] by Figure 4 Middle Presentation Layer Circle nodes With input layer The original node in For example, the calculation process for the weight of the inter-layer connection is as follows:

[0094] First, count the original nodes. The number of basic circles participating is 2; circle nodes The basic circle of subordinates is The original number of nodes is 3; and the basic circle is formed. All nodes , and The average number of basic circles involved is Therefore, the circle node With the original node The weight of the interlayer connection is 0.5926.

[0095] By analogy, the result can be calculated. Figure 4 The weights of all inter-layer connections.

[0096] V. Calculate the importance score

[0097] Based on the weights of the edges connecting different layers in the loop graph, the importance score of each original node is calculated; the specific steps are as follows:

[0098] S51, Formulating and Random walks between layers can be categorized into intra-layer random walks and cross-layer random walks; intra-layer random walks are... or Internally, nodes randomly transfer between each other; cross-layer random walks are divided into... arrive Upward random transfer and from Back The downward random transfer;

[0099] S52, calculated Adjacency transition matrix:

[0100] exist In the middle, assume the random walk is currently located at Then its next step will be to randomly transition to a state with equal transition probability. Neighbor set A certain circle of nodes Calculate the state transition probability and construct a system using the state transition probability as elements. adjacency transition matrix ;

[0101] The state transition probability is represented as follows:

[0102] ;

[0103] S53. Similarly, calculate according to the content in step S52. adjacency transition matrix ;

[0104] S54. Construct the adjacency shift matrix for cross-layer uplink random transitions:

[0105] from arrive When performing an upward random transfer, assume the random walk is currently located at... Then its next step will be randomly transferred to the corresponding upward transfer probability. ; Calculate the upward transition probability, and use the upward transition probability as elements to construct the transition from arrive Adjacency Upshift Matrix ;

[0106] The uplink transition probability is expressed as follows:

[0107] ;

[0108] S55. Construct the adjacency shift matrix for cross-layer downlink random transitions:

[0109] from arrive When performing a downlink random transfer, assume the random walk is currently at... Then its next step will be randomly transferred to the corresponding downlink transfer probability. ; Calculate the downlink transition probability, and construct a sequence using the downlink transition probability as elements from arrive Adjacency shift matrix ;

[0110] The downlink transition probability is represented as follows:

[0111] ;

[0112] S56. Combining intra-layer and inter-layer random walks to form multi-layer random walks: By fusing the adjacency transition matrix, adjacency upshift matrix, and adjacency downshift matrix, a complete multi-layer random walk transition matrix is ​​obtained: ;

[0113] S57, Set for time middle The access probability vector, then its Access probability vector at time step It is expressed as follows:

[0114] ;

[0115] S58. Determine if convergence has occurred and output the importance scores of the original nodes: If the convergence condition is met... If the condition is met, the iteration terminates; otherwise, the iteration continues. express and The second norm of the difference between them This represents the convergence threshold, with a value of 0.001.

[0116] The access probability vector of the original node obtained after convergence is used as the importance score of the original node.

[0117] VI. Acquiring a cluster of high-influence information dissemination nodes

[0118] Select those with the highest importance scores K A cluster of original nodes constitutes a high-influence information dissemination node cluster.

[0119] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for identifying high-influence information disseminators based on circle graph random walk, characterized in that, The method comprises the following identification steps: S1, obtaining a user list and relationship data between users in a current social scene, and constructing a user relationship network without direction and weight with the users as original nodes and the relationships between the users as edges; S2, obtaining all basic circles in the user relationship network, and mapping all the basic circles to corresponding circle nodes; S3, adding edges between the circle nodes by using a circle similarity matrix, and constructing a circle relationship network with the circle nodes and the corresponding edges; S4, connecting the circle nodes and the original nodes contained in the circle nodes by interlayer edges, and calculating the weights of the interlayer edges, so that the user relationship network and the circle relationship network are connected to form a circle graph; S5, calculating the importance score of each original node based on the weights of the interlayer edges in the circle graph; S6、selecting the top-ranked importance score K The original nodes constitute a high-influence information propagation node cluster. The calculation process of the importance score is as follows: S51, formulate and between the walk mode, including intra-layer random walk and cross-layer random walk; intra-layer random walk is in or inside, each node is randomly transferred between each other; cross-layer random walk is divided into uplink random transfer from to and downlink random transfer from back to ; S52, the calculation result the adjacent transition matrix: exist In the middle, assume the random walk is currently located at Then its next step will be to randomly transition to a state with equal transition probability. Neighbor set A certain circle of nodes Calculate the state transition probability and construct a system using the state transition probability as elements. adjacency transition matrix ; S53、Similarly, the content is calculated according to the content in step S52 adjacency transition matrix ; S54, constructing an adjacent up-moving matrix of cross-layer up-moving random transfer: From to When making an uplink random transition, let the random walker currently be at , then its next step will randomly transition to with the corresponding uplink transition probability. Calculate the uplink transition probability, and construct the adjacent uplink transition matrix from to with the uplink transition probability as the element ; S55, constructing an adjacent down-moving matrix of cross-layer down-moving random transfer: From to When making a down random transition, let the random walker be currently at , then its next step will be randomly transferred to with the corresponding down transition probability. The down transition probability is calculated, and the down transition probability is taken as an element to form the adjacent down transition matrix from to ;​ S56, combining intra-layer random walk and cross-layer random walk to form multi-layer random walk: by fusing the adjacent transition matrix, the adjacent up-shift matrix and the adjacent down-shift matrix, a complete multi-layer random walk transition matrix is obtained: ; S57、Set For The access probability vector at time In The access probability vector at time The access probability vector at time is represented as follows: ； S58, judging whether to converge and outputting the importance score of the original node: if the convergence condition is met , the iteration terminates, otherwise, the loop iteration is performed; represents the second order norm of the difference between and , represents the convergence threshold; The access probability vector of the original node obtained after convergence is taken as the importance score of the original node. 2.The method of identifying high-influence information disseminators based on circle graph random walk according to claim 1, characterized in that, The construction process of the user relationship network is as follows: S11, calling an open interface of a social platform to obtain a user list and relationship data between users; S12, structurally clean the relationship data, and model a network with users as original nodes and relationships between users as original edges, to form a user relationship network . 3.The method of claim 2, wherein, The obtaining process of the circle node is as follows: S21, selecting The original node with the maximum moderate centrality is selected as the root node, and a loop-free tree is generated by using a breadth-first tree search algorithm ; identify all original edges not contained in and mark them as non-tree edges; for each non-tree edge, find in the unique path connecting its two endpoints, which forms a basic cycle with the non-tree edge; find in all basic cycles in turn; S22, mapping all the basic circles to corresponding nodes by directly regarding the basic circles as nodes, and the nodes are called circle nodes.

4. The method of claim 3, wherein, The construction process of the circle relationship network is as follows: S31, calculating the circle adjacency similarity between two circle nodes respectively, and establishing a circle adjacency similarity matrix; S32, a negative operation is performed on the cycle adjacency similarity matrix, and a weighted undirected graph composed of cycle nodes is established with each element in the cycle adjacency similarity matrix after the negative operation as a weight; a minimum spanning tree connecting all cycle nodes is constructed in the weighted undirected graph on the premise of not forming a loop, and the minimum spanning tree with the smallest sum of weights is selected as the cycle relationship network .

5. The method of claim 4, wherein, The calculation formula of the circle adjacency similarity is as follows: ； In the formula, Indicates the first Each circle node; Indicates the first Each circle node; express and Cyclic adjacency similarity between them; express The set of edges consisting of all the original edges contained therein. express The set of edges consisting of all the original edges contained therein; express and The number of identical original edges contained within; express and The total number of categories of the original edges included.

6. The method of identifying high-influence information disseminators based on circle graph random walk according to any one of claims 1-5, characterized in that, The weight calculation formula of the interlayer edge is as follows: ； In the formula, denotes the weight of the inter-layer edge connecting and the original nodes ; denotes the number of basic circles participated by the original nodes; denotes the corresponding basic circle; denotes the number of original nodes in ; denotes the average value of the number of basic circles participated by all original nodes in ; .

7. The method of claim 6, wherein, The state transition probability is expressed as follows: ； wherein denotes the state transition probability from a random transition to a state; denotes the set of all edges in 8. The method of claim 7, wherein, The up-moving transition probability is expressed as follows: ； wherein denotes the uplink transition probability from to ; denotes the set of all cycle nodes connected to by inter-layer edges; denotes the weight of the inter-layer edge connecting and the cycle node .

9. The method of claim 8, wherein, The down-moving transition probability is expressed as follows: ； wherein denotes the transition probability from to ; denotes the original node; denotes the weight of the inter-layer edge connecting and .

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