Influence maximization method for realizing information propagation based on node feature fusion and community detection

Abstract

The invention discloses a method for realizing influence maximization of information propagation based on node feature fusion and community detection. The method comprises the following steps: step 1, dividing a network into relatively independent communities, and defining features and boundaries of different communities; selecting candidate nodes based on a community structure; step 2, candidate node selection: screening out a part of nodes with potential influence from numerous nodes to serve as an alternative set of seed nodes; by analyzing and evaluating various attributes of the nodes, candidate nodes connected with more other nodes in the network are selected; and step 3, community detection and seed node selection: selecting different types of nodes as seed nodes in each community according to characteristics and requirements to realize diversified propagation of information. The method has the advantage of being low in time consumption, and the purposes of increasing the information spreading range and improving the information spreading efficiency can be achieved.

Description

Technical Field

[0001] The present invention relates to the field of information dissemination technology, and in particular to a method for maximizing the influence of information dissemination based on node feature fusion and community detection. Background Art

[0002] Existing influence maximization methods face the critical challenges of a single measure of node influence and overlapping influence between seed nodes. This situation significantly reduces the accuracy and efficiency of influence maximization in important technical fields such as social network analysis, information dissemination optimization, and advertising strategies, severely hindering the development and application of related technologies. More specifically, traditional influence maximization research often employs a single metric to assess individual influence. These metrics may be based on structural characteristics of network topology, such as degree centrality (the number of nodes a node directly connects to), closeness centrality (the average distance from a node to other nodes in the network), and betweenness centrality (the frequency with which a node acts as a "bridge" within the network). While these single metrics can effectively assess individual influence in certain situations, they overlook the multidimensionality and complexity of influence and fail to fully reflect an individual's influence in different social contexts and network types. For example, an individual may have high influence within a close-knit community but relatively low influence within a broader social network. In real-world social networks, individual influence often overlaps and influences each other. An individual may simultaneously possess multiple different types of influence, such as professional influence, social influence, and emotional influence. Therefore, it is crucial to employ a multi-dimensional measurement approach to assess and maximize influence. This requires comprehensive consideration of factors such as an individual's position within the network, the strength of their relationships with other individuals, and the nature of the disseminated content. Furthermore, the influence of two or more nodes within a given area may intertwine, leading to reduced dissemination efficiency and wasted resources. Given the limitations of a single measurement approach and the phenomenon of overlapping influence, it is crucial to employ a multi-dimensional approach to assess node influence and, at the same time, to maximize it by eliminating overlap between nodes.

[0003] Existing technical solutions:

[0004] Some researchers have proposed an influence maximization method and system based on deep reinforcement learning and graph neural networks (CN119624685A). It aims to optimize the selection of seed nodes through reinforcement learning technology to maximize the dissemination of information in the network. A method and system for maximizing group influence in social networks based on Wk-shell has also been proposed (CN118229443A). This invention establishes the problem of maximizing group influence in social networks under an independent cascade model, with the goal of maximizing the number of activated groups in the social network, constructs an objective function, and uses the Wk-shell decomposition method to calculate the ks value of each node; the node with the largest number of covered groups is selected from the high ks nodes in turn as the seed node.

[0005] Existing technologies generally have the following shortcomings: 1) Single evaluation: Only a single centrality indicator is used, which cannot reflect the multi-dimensional influence characteristics of nodes; 2) Overlapping influence between seed nodes: The influence ranges of multiple seed nodes overlap, and the propagation effect is reduced; 3) Low efficiency: High computational complexity and lack of scalability in large-scale networks; 4) Limited scope of application: Existing methods often assume that the network is a connected graph, which makes it difficult to handle non-connected network structures. Summary of the Invention

[0006] In order to overcome the above technical problems, the purpose of the present invention is to provide an influence maximization method based on influential node identification and community detection to eliminate influence overlap, which has the characteristics of low time consumption and can achieve the purpose of increasing the scope of information dissemination and improving information dissemination efficiency.

[0007] The technical solution adopted in the present invention is:

[0008] A method for maximizing the influence of information dissemination based on node feature fusion and community detection includes the following steps:

[0009] Step 1: Community Detection and Candidate Node Selection: 1) Relationship with Information Dissemination Scope: By dividing the network into relatively independent communities, the characteristics and boundaries of different communities are clearly defined. Nodes within each community are closely connected and share similar characteristics and behavior patterns. Selecting candidate nodes within this structure ensures that representative and influential nodes are selected within each community. These nodes, as potential information disseminators, can better reach other nodes within their communities, thereby expanding the scope of information dissemination within each community. Due to the close connections between nodes within a community, information disseminates more quickly within the community, allowing more nodes to receive information, thereby increasing the scope of information dissemination throughout the network. 2) Relationship with Improving Information Dissemination Efficiency: Furthermore, selecting candidate nodes based on community structure avoids blind searching across the entire network. The entire network may contain a large number of nodes. Randomly selecting nodes as candidates without considering community structure can result in a dispersed distribution of selected nodes within the network, resulting in poor information dissemination. Community detection provides a foundation for candidate node selection, enabling more targeted selection of nodes within each community and narrowing the search space. This not only reduces unnecessary calculation and search costs, but also enables suitable candidate nodes to be found more quickly, laying the foundation for subsequent information dissemination, thereby improving the efficiency of information dissemination.

[0010] Step 2: Candidate Node Selection and Seed Node Selection: 1) Relationship with Information Propagation Scope: Candidate node selection involves screening a subset of potentially influential nodes from a large number of nodes to serve as a candidate set of seed nodes. By analyzing and evaluating various node attributes, such as their degree, we select candidate nodes that are highly connected to other nodes in the network. Once these candidate nodes are designated as seed nodes, they leverage their high connectivity to spread information to more neighboring nodes. As information continues to spread, its reach gradually expands, encompassing more nodes. 2) Relationship with Improving Information Propagation Efficiency: Furthermore, analyzing and evaluating node attributes provides additional reference for seed node selection, making the final selection more rational and effective. Appropriate seed node selection means that information can be propagated more efficiently across the network, starting from these key nodes. For example, by selecting nodes with high degrees as seed nodes, information can be propagated to multiple nodes at once, rather than node by node. This significantly reduces information propagation time and path length, thereby improving information propagation efficiency.

[0011] Step 3: Community Detection and Seed Node Selection: 1) Relationship with Information Dissemination Scope: Community detection helps identify the characteristics and boundaries of different communities, providing clearer guidance for seed node selection. Selecting different types of nodes as seed nodes within each community, based on their characteristics and needs, can achieve diversified information dissemination. Different types of nodes play different roles within a community. Some may be core nodes, closely connected to other nodes; others may be edge nodes, capable of transmitting information to other communities. By carefully selecting these different types of seed nodes, information can be fully disseminated within the community and flow and diffuse across community boundaries, further expanding the scope of information dissemination. 2) Relationship with Improving Information Dissemination Efficiency: Furthermore, selecting seed nodes based on the structure and connectivity between communities can facilitate the flow and diffusion of information across communities. Intercommunity connectivity provides channels for cross-community information dissemination. By selecting appropriate seed nodes, these connections can be fully utilized, ensuring smoother information transmission between communities. This prevents excessive concentration or stagnation of information within a particular community, improving the speed and efficiency of information dissemination throughout the network.

[0012] In step 1, during the community detection phase, the network is divided into multiple relatively independent communities through community detection, which greatly reduces the search space. This reduces unnecessary searches and calculations, thereby improving the efficiency of information dissemination. This method uses the Louvain algorithm for community partitioning, which identifies community structures in the network by iteratively optimizing modularity.

[0013] The Louvain algorithm consists of three steps: initial community allocation, local optimization, and community merging. Small communities below a set threshold are merged into the community with the most adjacent nodes. The formula for the community size threshold is as follows:

[0014] C size =ω×|V(G)|

[0015] Among them, C size represents the community size threshold, below which communities are merged. |V(G)| represents the number of nodes in network G, reflecting the overall size of the network. A larger network size means a wider potential range for information dissemination, but it also may incur higher search and computational costs. ω is an adjustable parameter that controls the scale of community merging. When ω is appropriately valued, it ensures that small communities below the set threshold are merged into the community with the most neighboring nodes. This operation avoids excessive and ineffective searching within small communities, allowing information to be more concentrated in potentially large communities or key connected areas, thereby expanding the scope of information dissemination.

[0016] For example, in some social networks, if a small community has low user activity but is closely connected to other larger communities, merging communities can help information spread more quickly from the larger community to these previously dispersed smaller community nodes, allowing more users to receive the information and thus expanding the reach of information throughout the social network. Furthermore, from the perspective of improving information dissemination efficiency, by properly setting ω and controlling the size of community merging, unnecessary search and computation are reduced. Before community detection and merging, searching for influential nodes as candidate nodes across the entire network requires traversing a large number of nodes and calculating various attributes for each node, a time-consuming task. However, the Louvain algorithm, which divides and merges communities based on a community size threshold formula, significantly reduces the search space. This allows for more targeted selection of representative and influential nodes within each relatively independent and appropriately sized community, avoiding blind searches across the entire complex network, saving significant computing resources and time, and significantly improving information dissemination efficiency. For example, in a large information dissemination network, without community division, it might be necessary to traverse tens of thousands of nodes to calculate their influence. However, after dividing communities using the Louvain algorithm, calculations and screening only need to be performed within each smaller community, significantly shortening the initial preparation work for information dissemination, allowing information to enter the dissemination stage more quickly, and improving overall dissemination efficiency.

[0017] In step 2, during the candidate node selection phase, a new hybrid node influence measurement method based on NGC nodes, NGH, is proposed. This method selects nodes with higher potential influence as candidate nodes, allowing limited resources to be concentrated on these candidate nodes that are more likely to become effective seed nodes, thus avoiding resource waste. The NGC node is the node with the highest centrality closest to each node.

[0018] The specific implementation process of the NGH method includes two steps:

[0019] (1) First, three different centrality indices are selected: semi-local centrality (LC), structural hole (SH), and mixed degree decomposition (MDD). LC selects nodes that are connected to many nodes and can directly transmit information to a large number of neighboring nodes. MDD selects nodes that may be the connection points of different groups or communities and can transmit information from one group to another. SH selects nodes that can connect groups of nodes that are not originally connected, thus achieving cross-group information dissemination.

[0020] (2) Secondly, the NGC node corresponding to each node is selected based on each centrality indicator. The frequency of each node as an NGC node is a key indicator for selecting candidate nodes. After these nodes are selected as candidate nodes, when they act as seed nodes for information dissemination, they can transmit information to a wider network area, thereby expanding the scope of information dissemination. Because nodes with different centralities are often connected to different node groups in the network, by comprehensively considering these nodes, information can break through the limitations of a single group and spread to more nodes that were originally difficult to reach.

[0021] The process of determining candidate nodes is as follows: First, find the NGC node of each node based on the LC, SH and MDD methods respectively. Secondly, count the total frequency of each NGC node in the LC, SH and MDD methods, and then select candidate nodes in descending order according to the frequency of NGC nodes. Since only the frequency of NGC nodes is concerned, complex and comprehensive analysis of all nodes is avoided, thereby reducing the amount of calculation and search time. Compared with the traditional single metric method, this hybrid method can more accurately find potential key nodes and concentrate limited resources on these candidate nodes that are more likely to become effective seed nodes, avoiding waste of resources and thus improving the efficiency of information dissemination. By comprehensively considering multiple indicators, the NGH method can more comprehensively evaluate the influence of nodes, making it more likely that the selected candidate nodes will effectively disseminate information, reducing the obstacles to information dissemination caused by the selection of inappropriate nodes, and improving the overall dissemination efficiency.

[0022] The number of candidate nodes is twice the number of seed nodes. If the number of NGC nodes is less than the number of candidate nodes, non-NGC nodes need to be selected as candidate nodes. The rule for selecting non-NGC nodes is: according to the node centrality results of the LC, SH, and MDD methods, all nodes are ranked from high to low, and the highest-ranked non-NGC nodes are randomly selected as candidate nodes. Such nodes have relatively high influence and greater potential for disseminating information, which helps to expand the scope of information dissemination. If all three nodes at a certain location are NGC nodes, the search continues for the next location until 2k candidate nodes are obtained, where k is the number of seed nodes. The selected candidate nodes include not only the focal nodes at the center of the network and the key nodes at the periphery of the network, but also nodes that act as bridges in the network. This initiative breaks through the limitations of traditional single measurement methods.

[0023] In addition, in order to more accurately select high-potential candidate nodes, the actual influence of the nodes in the network can be measured. The present invention proposes another new candidate node selection method from a different perspective: the node importance measurement method (NRP importance). This measurement method can not only select suitable candidate nodes but also reduce the redundancy of information dissemination, because the screened candidate nodes have a certain degree of representativeness and uniqueness in the network, and the information they disseminate can cover different node groups, avoiding repeated dissemination of information. Specifically, this method is used to rank the importance of nodes. The higher the NRP value of the node, the higher its ranking, indicating that it has greater influence in the network. The NRP measurement not only takes into account the network topological properties of the node, such as the degree and clustering coefficient of the node, but also takes into account the role of the node in the network, that is, its functional role. In other words, the NRP measurement method can more accurately measure the actual information dissemination ability of the node in the network, provide a more accurate node selection basis for the influence maximization problem, and thus help to speed up the spread of information in the network. The measurement consists of two parts: topological importance (TI) and functional importance (FI), which can work together to more effectively disseminate information. The formula is as follows:

[0024] NRP m =NTI m +θ*NFI m

[0025] Among them, θ represents the weight coefficient, which is used to balance the topological importance of node m NTI m and functional importance NFI m The relative contribution of node influence. Topological importance can avoid redundant and ineffective information dissemination by selecting important nodes for information dissemination, thereby improving the accuracy and efficiency of information dissemination. Functionally important nodes can promote information sharing and innovation in the process of information transmission between different groups. m Taking into account the topological importance of the node itself, the importance of its first-order neighbors, and the importance of its second-order neighbors, the overall topological importance of a node is calculated as follows:

[0026] NTI m =α*TI m +β*FTI m +γ*STI m

[0027] Among them, α, β, and γ are weight coefficients, which adjust TI m , FTI m and STIs m Relative contribution to the final importance, where the importance of the first-order neighbors FTI m That is, the information dissemination ability of directly connected nodes, the importance of second-order neighbors STIm That is, the neighbors of the neighbors, reflecting the node's indirect information dissemination ability in the entire network. If most of a node's neighbors are important nodes, then the node also plays an important role in information dissemination. This is because when information propagates in the network, important neighboring nodes can further pass the information to more other nodes, thereby expanding the scope of information dissemination. The present invention can identify nodes that occupy key positions in the network topology. These nodes become key hubs for the rapid dissemination of information due to their rich connectivity and extensive influence on the surrounding areas. m , FTI m and STIs m The calculation formula is as follows:

[0028]

[0029] Where Δm represents the number of triangles generated by node m, |Γ m | represents the number of first-order neighbors of node m. Both are important indicators that directly measure the ability of information dissemination. A highly connected node means it has more direct information dissemination channels. From the perspective of information dissemination, such a node can quickly transmit information to its many neighbors, thus forming an efficient information diffusion center in the local area of the network. mm It represents the distance from node m to itself, which is 0 here, d mn Indicates the distance from node m to its first-order neighbor, which is 1 here; d mz It represents the distance from node m to its second-order neighbor, which is 2 here. A shorter distance means that information can reach the target node faster, reducing transmission time and energy consumption. A longer distance may lead to increased delays in information transmission and information attenuation, thereby increasing the cost and time delay of information dissemination. The NRP metric uses the structural hole coefficient sh of the node to quantify the functional importance FI of the node; nodes with high structural hole coefficients are usually located in the "bridge" position between different groups or communities, and can connect groups of nodes that were originally not very connected, realizing cross-group dissemination of information. Therefore, functionally important nodes play the role of "connectors" and "bridges" in information dissemination, which helps to expand the scope of information dissemination. Functional importance NFI of node m m The calculation is as follows:

[0030]

[0031] Calculate the NRP importance of each node. Select the top 2,000 nodes with the highest NRP values as another set of candidate nodes. This ensures that the selected nodes are representative and unique in the network. These nodes not only occupy a dominant position in the topology but also play an important role in terms of functionality, covering different node groups.

[0032] In step 3, during the seed node selection phase, the first step is to screen out the common nodes between the two sets of candidate nodes (theoretically, a total of 4,000 candidate nodes). These common nodes are the key bridges connecting two different communities or groups. Their existence helps information flow between different communities, thereby expanding the scope of information dissemination. Highly influential seed nodes usually have a wide social circle, high reputation and trust, and their information is more easily accepted and spread by other nodes. Therefore, selecting these highly influential nodes as seed nodes can ensure that the information gains greater dissemination momentum in the initial stage, because they are more likely to be accepted and spread by other nodes.

[0033] (1) If the number of public nodes obtained is exactly equal to k, then this set of public nodes is the final set of seed nodes. In this case, since public nodes are nodes that exist in both candidate node sets, their connectivity and influence in the network are relatively large, and they can serve as the initial propagation source to quickly spread information to a wider range of nodes. From the perspective of the scope of information propagation, these public nodes can reach other related nodes in the two candidate node sets, thereby expanding the initial propagation range of information; from the perspective of improving the efficiency of information propagation, due to the influence and connectivity of these nodes themselves, information can be transmitted to more nodes in a shorter time, reducing the time cost of propagation;

[0034] (2) If the number of public nodes obtained is less than k, the probability of non-public nodes being selected as seed nodes is calculated, and the top several candidate nodes with the highest probability will be selected as the final required seed nodes until the number requirement is met. This step involves multiple factors such as the information entropy, clustering coefficient, influence overlap index (OI) of candidate nodes, and common neighbors between candidate nodes. An innovative method for identifying seed nodes from candidate nodes is proposed. In particular, the determination of the influence overlap index takes into account the basic topological properties of the network. At the same time, the influence overlap between seed nodes is reduced. Among them, information entropy reflects the richness and uncertainty of the information carried by the node. The higher the information entropy, the more diverse the information contained in the node, which can provide more value in the process of information dissemination, attract more attention from other nodes, and thus help expand the scope of information dissemination. The clustering coefficient is used to measure the degree to which nodes tend to cluster together. Nodes with higher clustering coefficients also have higher connectivity between their neighboring nodes, forming a close community structure. In such a community, information dissemination is more efficient because the close connection between nodes allows information to spread quickly within the community and then spread to a larger network through the connection between communities. Nodes with a large number of common neighbors occupy a more important position in the network and have closer connections with other nodes. When such nodes are used as seed nodes, they can quickly spread information with the help of their many common neighbors, thereby increasing the speed and scope of information dissemination. The influence overlap index comprehensively considers the basic topological properties of the network. It reflects the degree of overlap of the influence of a node with other nodes in the network. By reducing the influence overlap between seed nodes, the repeated dissemination of information can be avoided and the efficiency of information dissemination can be improved. For example, if the influence overlap of two seed nodes is high, they will disseminate the same information to the same neighboring nodes, which will result in a waste of resources and reduce the efficiency of dissemination. Selecting nodes with a lower influence overlap index as seed nodes can enable information to be more effectively disseminated in different regions and node groups, thereby expanding the scope of information dissemination.

[0035] (3) In addition, if the number of public nodes obtained is greater than k, some nodes need to be removed. Specifically, first sort the nodes in the community in descending order according to the number of nodes in the community. This helps to identify which communities have more concentrated nodes and may form a tighter information dissemination network. Secondly, determine which communities this group of nodes belongs to. If there are more than or equal to 2 nodes in the same community, randomly select a node from the community and leave it, so that in the end there are only less than or equal to 1 public node in each community as a seed node. This can reduce the redundant dissemination of information within the same community and improve the efficiency of information dissemination across communities. Then, count the number of seed nodes in all communities. If it is k, the seed node selection ends; if it is less than k, the processing method is the same as the case where the number of public nodes is less than k, except that the remaining public nodes are counted here; if it is greater than k, remove nodes from the minimum community size until the number of nodes meets the requirement. In general, selecting seed nodes from high-potential candidate nodes can improve the quality of seed node selection and increase the scope of information dissemination.

[0036] Beneficial effects of the present invention:

[0037] In summary, the present invention can accurately identify key nodes in a complex network environment and maximize the effect of information dissemination. For example, in social network analysis, accurately identifying nodes with high influence is crucial for the rapid dissemination of information and the guidance of public opinion. The method of the present invention can be applied to analyze user relationships and behavioral data in social networks. By integrating multiple measurement methods, analyzing the basic topological properties of the network and other technical means, it can more accurately find those nodes that can play a key role in information dissemination, thereby providing strong support for content recommendation, advertising placement and other services of social media platforms, and improving the efficiency and effectiveness of information dissemination.

[0038] (1) Higher efficiency: By identifying key influential nodes and eliminating the overlapping influence between seed nodes, unnecessary resource waste can be reduced and the overall influence propagation effect can be improved.

[0039] (2) Higher market value: It can locate key influencers more accurately, making resource allocation more concentrated and precise. For example, in commercial marketing, when promoting new products or services, this method can be used to identify potential key consumers and formulate more effective market entry strategies; in public health, such as disease control and prevention, by identifying key communicators, the transmission chain can be more effectively cut off and the spread of the disease can be slowed down; in policy propaganda, the government or public institutions can use this technology to optimize the dissemination path of policies or public information to ensure effective coverage of information. In summary, the influence maximization strategy based on the present invention can bring significant market advantages to enterprises and organizations, improve the return on advertising and promotional activities, and reduce costs. In addition, for the fields of public safety and health, this method can provide a more effective disease and information management tool with significant social value and economic benefits.

[0040] (3) Better adaptability: This method can be adjusted according to different application scenarios and optimized according to specific network structures and goals. It is applicable to connected and disconnected networks and has good scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A sample network containing 20 nodes is randomly generated.

[0042] Figure 2 It is a community formed after local optimization.

[0043] Figure 3 It is the community finally formed after iteration.

[0044] Figure 4 An example of the process of finding an NGC node for a node.

[0045] Figure 5 Information propagation results of different influence maximization methods with different seed sizes on 16 networks.

[0046] Figure 6 Information propagation results of different influence maximization methods under different propagation probabilities on 16 networks. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] This paper proposes a novel influence maximization method based on influential node identification and community detection to eliminate influence overlap. The method consists of three steps: community detection, candidate node selection, and seed node selection. Seed nodes are the influential nodes that are finally identified and used to achieve the widest possible dissemination effect in the network.

[0049] Specifically, in the community detection phase, the method uses the Louvain algorithm to perform community division, which identifies the community structure in the network by iteratively optimizing the modularity. This process not only reduces the search space, but also lays the foundation for reducing the influence overlap between seed nodes. The Louvain algorithm is divided into three steps: initial community assignment, such as Figure 1 As shown; local optimization, such as Figure 2 As shown; the merger of societies, such as Figure 3 However, the communities divided by the Louvain algorithm may have the problem of small community size. If there are a large number of seed nodes, some communities may need to select multiple seed nodes, and small communities often have limited contribution to overall information dissemination. Therefore, it is necessary to merge small communities below a set threshold into the community with the most adjacent nodes. The formula for the community size threshold is as follows:

[0050] C size =ω×|V(G)|

[0051] Among them, C size represents the community size threshold, below which communities are merged. |V(G)| represents the number of nodes in the network G, and ω represents an adjustable parameter used to control the size of community mergers. This paper sets it to 0.01, which is commonly used.

[0052] In the candidate node selection stage, a new hybrid node influence measurement method NGH based on NGC nodes is proposed. Among them, the NGC node is the node with the largest centrality closest to each node. The selection process is as follows: Figure 4 As shown. By screening a portion of more promising nodes as candidate sets, NGH can significantly reduce the number of nodes that need to be traversed and calculated during the seed node selection process, thereby significantly reducing the computational complexity. The specific implementation process of the NGH method includes two steps: (1) First, three different centrality indicators are selected, namely semi-local centrality (LC), structural hole (SH) and mixed degree decomposition (MDD); (2) Secondly, the NGC node corresponding to each node is selected according to each centrality indicator. The frequency of each node as an NGC node is the key indicator for selecting candidate nodes.

[0053] Unlike other candidate node selection methods, this method selects candidate nodes by identifying NGC nodes with high centrality among their neighbors. The process for determining candidate nodes is as follows: First, the NGC node for each node is found using the LC, SH, and MDD methods. Second, the total frequency of each NGC node appearing in the LC, SH, and MDD methods is counted. Candidate nodes are then selected in descending order of NGC node frequency. In this method, the number of candidate nodes is twice the number of seed nodes. If the number of NGC nodes is less than the number of candidate nodes, non-NGC nodes are selected as candidate nodes. The rule for selecting non-NGC nodes is: all nodes are ranked from high to low based on the node centrality results of the LC, SH, and MDD methods, and the highest-ranked non-NGC node is randomly selected as a candidate node. If all three nodes at a given location are NGC nodes, the search continues until 2k candidate nodes are obtained, where k is the number of seed nodes. The selected candidate nodes include not only focal nodes at the network center and key nodes at the periphery, but also nodes that serve as bridges within the network. This approach overcomes the limitations of traditional single-metric methods.

[0054] In addition, in order to more accurately select high-potential candidate nodes, thereby measuring the actual influence of the nodes in the network. The present invention proposes another new candidate node selection method from a different perspective: node importance measurement method (NRP importance). This method is used to rank the importance of nodes. The higher the NRP value of the node, the higher its ranking, indicating that it has greater influence in the network. The NRP measurement not only takes into account the network topological properties of the node, such as the degree and clustering coefficient of the node, but also takes into account the role of the node in the network, that is, its functional role. In other words, the NRP measurement method can more accurately measure the actual influence of the node in the network, and provide a more accurate node selection basis for the influence maximization problem. The metric consists of two parts: topological importance (TI) and functional importance (FI), and the formula is as follows:

[0055] NRP m =NTI m +θ*NFI m

[0056] Among them, θ represents the weight coefficient, which is used to balance the topological importance of node m NTI m and functional importance NFI m The relative contribution to the node's influence. In this chapter, we take θ = 1, assuming that topological importance and functional importance are equally important. m Taking into account the topological importance of the node itself, the importance of its first-order neighbors, and the importance of its second-order neighbors, the formula for calculating the overall topological importance of the node can be obtained:

[0057] NTIm =α*TI m +β*FTI m +γ*STI m

[0058] Among them, α, β, and γ are weight coefficients, which adjust TI m , FTI m and STIs m Relative contribution to the final importance. In the present invention, these weights are 1, because the calculation of TI m , FTI m and STIs m has passed the exponential decay factor e d The contribution of distant neighbors is adjusted so that their contribution to the node's influence gradually decreases. This mechanism is consistent with the laws of information dissemination and influence diffusion in reality, that is, neighbors far away from the node contribute relatively less to its influence. m , FTI m and STIs m The calculation formula is as follows:

[0059]

[0060] Where Δm represents the number of triangles generated by node m, |Γ m | represents the number of first-order neighbors of node m, d mm It represents the distance from node m to itself, which is 0 here, d mn Indicates the distance from node m to its first-order neighbor, which is 1 here; d mz It represents the distance from node m to its second-order neighbors, which is 2 here. In order to comprehensively measure the importance of the node, the NRP metric uses the structural hole coefficient sh of the node to quantify the functional importance FI of the node. Similar to the topological importance NTI, the functional importance also takes into account the first-order neighbors and second-order neighbors of the node to more comprehensively evaluate the cross-community influence of the node. Therefore, the functional importance NFI of node m is m The calculation is as follows:

[0061]

[0062] Calculate the NRP importance of each node. Select the top 2k nodes with the largest NRP values as another set of candidate nodes. This measurement method can effectively solve the problem of monotonicity in node ranking, improve the quality of seed node selection, and thus maximize the overall influence.

[0063] In the seed node selection stage, the present invention first screens out the common nodes in the two sets of candidate node sets (theoretically a total of 4k candidate nodes). (1) If the number of common nodes obtained is exactly equal to k, then this set of common nodes is the final set of seed nodes required. (2) If the number of common nodes obtained is less than k, the probability of non-public nodes being selected as seed nodes is calculated, and the top several candidate nodes with the highest probability will be selected as the final required seed nodes until the number requirement is met. This step involves multiple factors such as the information entropy, clustering coefficient, influence overlap index (OI) of candidate nodes, and common neighbors between candidate nodes, and proposes an innovative method for identifying seed nodes from candidate nodes. In particular, the determination of the influence overlap index comprehensively considers the basic topological properties of the network. At the same time, the influence overlap between seed nodes is reduced. (3) In addition, if the number of common nodes obtained is greater than k, some nodes need to be removed. Specifically, first sort in descending order according to the number of nodes in the community. Next, determine the communities in which this group of nodes resides. If there are two or more nodes in the same community, randomly select a node from that community and keep it, so that ultimately each community has only one or less public nodes as seed nodes. Next, count the number of seed nodes within all communities. If it is k, seed node selection ends. If it is less than k, the process is the same as when the number of public nodes is less than k, except that the remaining public nodes are counted. If it is greater than k, nodes are removed from the minimum community size until the required number of nodes is met. In general, selecting seed nodes from high-potential candidate nodes can improve the quality of seed node selection and increase the spread range.

[0064] The present invention embodies methods for improving information dissemination efficiency: 1) Reducing the search space (community detection). Before community detection, the entire network as a whole has a large number of nodes, and the information dissemination paths are complex and diverse. A large number of nodes must be traversed to find suitable seed nodes, resulting in high computational costs and low efficiency. However, by using community detection to divide the network into multiple relatively independent communities, the search space is greatly reduced. When selecting seed nodes within each community, only the nodes within that community need to be considered, reducing unnecessary searches and calculations, thereby improving information dissemination efficiency. 2) Optimizing resource allocation (candidate node selection). The candidate node selection process analyzes various node attributes and characteristics to select nodes with high potential influence as candidates. This allows limited resources (such as computing resources and time resources) to be concentrated on candidate nodes that are more likely to become effective seed nodes, avoiding resource waste. Furthermore, selecting suitable candidate nodes can reduce information dissemination redundancy. Because the selected candidate nodes are representative and unique in the network, the information they disseminate can reach different node groups, avoiding duplicate information dissemination. 3) Ensuring Starting Point Validity (Seed Node Selection): Choosing appropriate seed nodes is key to ensuring that information spreads quickly and effectively across the network. Highly influential seed nodes typically have extensive social networks, high reputations, and high levels of trust, making their information more easily accepted and disseminated by other nodes. Therefore, by carefully selecting seed nodes, information can gain significant initial momentum, spreading rapidly across the network and reaching more nodes.

[0065] The key points of this discovery are as follows: 1) Dual-group candidate node selection mechanism: This paper proposes two candidate node selection methods to improve the accuracy of seed node selection; 2) Multi-centrality fusion mechanism (LC+SH+MDD): This paper combines the advantages of different centrality methods to identify key nodes, considering not only important nodes in the network center and key nodes in the network periphery, but also nodes that play a bridging role in the network; 3) NGC node mechanism: This paper selects candidate nodes by identifying the nearest neighbor nodes with the maximum centrality; 4) Introduction of NRP metric: This metric consists of two parts: topological importance and functional importance of nodes. Topological importance focuses on topological features such as node degree and clustering coefficient, reflecting the importance of nodes in the social The central role within the group; the functional importance quantifies the bridging ability of the node at the edge of the community with the help of the structural hole coefficient. The NRP metric can effectively solve the monotonicity problem of node ranking; 5) Influence overlap index design (OI index): considering the number of candidate nodes in its second-order neighborhood and the distance to other candidate nodes, accurately modeling the overlap of node propagation range, improving the efficiency and effectiveness of information dissemination; 6) Diffusion range evaluation: the present invention evaluates the possibility of each candidate node being selected as a seed node. This possibility takes into account multiple factors, including the information entropy, clustering coefficient and influence overlap index of the candidate node, as well as the common neighbors between candidate nodes; 7) Community detection: reduces the search space and effectively reduces the time complexity.

[0066] Practical Application:

[0067] To evaluate the effectiveness of our proposed influence maximization method, named NOIRX, we conducted extensive and comprehensive experiments on multiple real and artificial networks using datasets from the Network Repository. The specific characteristics are shown in Tables 1 and 2. We also selected eight classic and state-of-the-art benchmark methods for comparison, as shown in Table 3.

[0068] Table 1: Basic information of the real-world network used in this invention

[0069]

[0070] Table 2: Basic information of the artificial network used in this invention

[0071]

[0072] Table 3: Summary of baseline methods

[0073]

[0074] This paper uses the IC model to simulate the propagation process of seed nodes selected by various influence maximization methods. The propagation probability in the IC model is set to the commonly used 0.01. To ensure a fair comparison, the influence propagation range of the seed nodes selected by each influence maximization method was calculated through 10,000 Monte Carlo simulations, hereinafter referred to as SC.

[0075] Figure 5 Experimental results of different influence maximization methods on multiple real and artificial networks are presented. The horizontal axis represents the number of selected seed nodes, and the vertical axis represents their propagation capacity, defined as the average number of activated nodes in the network. As can be seen from the figure, NOIRX achieves optimal or near-optimal propagation capacity across all networks compared to the best baseline method, reflecting its effectiveness. Across all experimental networks, its influence significantly increases with the number of seed nodes. However, performance varies across different numbers of seed nodes. More specifically, the CC method selects seed nodes with the worst propagation capacity in almost all networks. Influence maximization methods with similar performance to CC are CNC+ and KSIF, which slightly outperform CC on most networks but still lag behind the other baseline methods overall. Although the SC growth trends of NOIRX and the baseline methods are similar across all networks, NOIRX significantly outperforms the baseline methods in most networks.

[0076] In networks such as Grid1, PTC-MM, and PTC-FM, NOIRX outperforms other methods at almost all seed node scales, such as Figure 5 (a), (h) and (i). In Minnesota, Grid2 and SW4 networks, when the seed node size is small, NOIRX is not optimal, but its SC grows faster than other methods, such as Figure 5 (e), (g), and (n). In addition, in networks such as DD244 and Scfxm1, when the seed node scale is small, NOIRX outperforms all other baseline methods, but when the seed node scale is large, NOIRX is no longer the best, but is second only to the DD method, as shown in Figure 5 As shown in (b) and (c). Figure 5 (k) and (l) show the experimental results on the SW1 and SW2 networks, respectively. The results show that due to the smaller network size, the difference in experimental results between NOIRX and the baseline method is small. However, it is obvious from the details in the magnified rectangular area that NOIRX's results are significantly better than the baseline method.

[0077] In summary, NOIRX demonstrates good performance across all networks, demonstrating that it is a robust and reliable influence maximization optimization method. Furthermore, experimental results demonstrate that selecting candidate nodes based on multiple centrality methods and considering multiple factors during the propagation process to reduce influence overlap among candidate nodes is an effective strategy.

[0078] The propagation probability p of the IC model has a significant impact on the influence propagation process. By using different propagation probabilities to evaluate the influence maximization method, its adaptability and robustness in different environments can be verified. In order to make the experiment reasonable and complete, for different numbers of seed nodes, it is necessary to evaluate the propagation range of seed nodes selected by different influence maximization methods under different propagation probabilities on each network. However, for simplicity, Figure 6 Only the experimental results of each network with a specific number of seed nodes are shown. The horizontal axis is the propagation probability, and the vertical axis is still the propagation capacity of the seed nodes.

[0079] It can be seen that NOIRX generally outperforms the baseline methods on all networks. More specifically, on the Grid1 network, NOIRX performs best, while DD and H-index* are slightly inferior, while the performance of other baseline methods is significantly worse than DD, H-index* and NOIRX, such as Figure 6 (a) shows that among DD244, Euroroad, Minnesota, Dual and six artificial networks, NOIRX performs the best, while CC performs the worst. Figure 6 (b), (d), (e) and (k)-(p) are shown. On PTC-MM, PTC-FM and PTC-FR networks, NOIRX still performs the best, DD and DC are slightly inferior, and ECRM performs the worst, as shown in Figure 6 (h), (i) and (j). On the SW1 network, if Figure 6 As shown in (k), NOIRX performs significantly better than other methods, followed by H-index* and DD. ERM ranks fourth, followed by ECRM and KSIF, while CC performs the worst. Figure 6 (c) and (f) show the experimental results of Scfxm1 and Dual network respectively. The results show that the SC difference between NOIRX and the baseline method is not significant, but NOIRX still outperforms other methods.

[0080] In summary, although the performance differences between the methods are not significant, it can be seen that NOIRX's SC still has advantages over the baseline methods. In addition, when the propagation probability p is high, especially when it exceeds 0.1, the SC of all methods is improved because the propagation range of the seed node in the stable state almost covers the entire network. Overall, Figure 6 It shows that when the scale of seed nodes is the same, the propagation range of the NOIRX method is significantly better than other baseline methods.

[0081] In general, the influence maximization method proposed in this invention can significantly improve the scope of information dissemination.

Claims

1. A method for maximizing the influence of information dissemination based on node feature fusion and community detection, characterized in that: The following steps are included: Step 1: By dividing the network into relatively independent communities, the characteristics and boundaries of different communities are clarified; candidate nodes are selected based on the community structure; Step 2: Candidate node selection involves selecting a subset of potentially influential nodes from a large number of nodes as candidate seed nodes. By analyzing and evaluating various node attributes, candidate nodes that are connected to a large number of other nodes in the network are selected. Step 3: Community detection and seed node selection: In each community, different types of nodes are selected as seed nodes according to their characteristics and needs to achieve diversified information dissemination.

2. The method for maximizing the influence of information dissemination based on node feature fusion and community detection according to claim 1 is characterized in that: In step 1, in the community detection phase, after the network is divided into multiple relatively independent communities through community detection, the Louvain algorithm is used for community division. The algorithm identifies the community structure in the network by iteratively optimizing the modularity. The Louvain algorithm consists of three steps: initial community allocation, local optimization, and community merging. Small communities below a set threshold are merged into the community with the most adjacent nodes. The formula for the community size threshold is as follows: C size =ω×|V(G)| Among them, C size represents the community size threshold. Communities below this threshold need to be merged. |V(G)| represents the number of nodes in the network G. ω is an adjustable parameter used to control the scale of community mergers. When ω is reasonably set, it can ensure that small communities below the set threshold are merged into the community with the most adjacent nodes.

3. The method for maximizing the influence of information dissemination based on node feature fusion and community detection according to claim 1 is characterized in that: In step 2, during the candidate node selection phase, a hybrid node influence measurement method NGH based on NGC nodes is used; wherein the NGC node is the node with the largest centrality closest to each node; The specific implementation process of the NGH method includes two steps: (1) First, three different centrality indices are selected, namely semi-local centrality (LC), structural hole (SH) and mixed degree decomposition (MDD); (2) Secondly, the NGC node corresponding to each node is selected according to each centrality index. The frequency of each node as an NGC node is the key indicator for selecting candidate nodes.

4. The method for maximizing the influence of information dissemination based on node feature fusion and community detection according to claim 3 is characterized in that: The process of determining candidate nodes is as follows: First, the NGC node of each node is found based on the LC, SH and MDD methods respectively; Secondly, the total frequency of each NGC node in the LC, SH and MDD methods is counted, and then the candidate nodes are selected in descending order according to the frequency of NGC nodes. The number of candidate nodes is twice the number of seed nodes. If the number of NGC nodes is less than the number of candidate nodes, non-NGC nodes need to be selected as candidate nodes. The rule for selecting non-NGC nodes is: according to the node centrality results of LC, SH and MDD methods, all nodes are ranked from high to low, and the highest-ranked non-NGC nodes are randomly selected as candidate nodes. If all three nodes at a certain location are NGC nodes, the search continues for the next location until 2k candidate nodes are obtained, where k is the number of seed nodes. The selected candidate nodes include not only the focal nodes at the center of the network and the key nodes at the periphery of the network, but also the nodes that act as bridges in the network.

5. The method for maximizing the influence of information dissemination based on node feature fusion and community detection according to claim 4 is characterized in that: Candidate node selection method: Node importance measurement method (NRP importance), which consists of two parts: topological importance (TI) and functional importance (FI). The formula is as follows: <h2 style=";text-align:left;direction:ltr">NRP<h2 style=";text-align:left;direction:ltr"> m <h2 style=";text-align:left;direction:ltr"> (NTI)<h2 style=";text-align:left;direction:ltr"> m <h2 style=";text-align:left;direction:ltr"> +θ*NFI<h2 style=";text-align:left;direction:ltr"> m Among them, θ represents the weight coefficient, which is used to balance the topological importance of node m NTI m and functional importance NFI m Relative contribution to node influence, NTI m Taking into account the topological importance of the node itself, the importance of its first-order neighbors, and the importance of its second-order neighbors, the overall topological importance of a node is calculated as follows: NTI m =α*TI m +β*FTI m +γ*STI m Among them, α, β, and γ are weight coefficients, which adjust TI m , FTI m and STI m Relative contribution to the final importance, where the importance of the first-order neighbors FTI m That is, the information dissemination ability of directly connected nodes, the importance of second-order neighbors STI m That is, the neighbors of the neighbors, which reflects the indirect information dissemination ability of the node in the entire network. If most of the neighbors of a node are important nodes, then the node also plays an important role in information dissemination; FI m , FTI m and STIs m The calculation formula is as follows: Where Δm represents the number of triangles generated by node m, |Γ m | represents the number of first-order neighbors of node m; d mm It represents the distance from node m to itself, which is 0 here, d mn Indicates the distance from node m to its first-order neighbor, which is 1 here; d mz It represents the distance from node m to its second-order neighbor, which is 2 here. The NRP metric uses the structural hole coefficient sh of the node to quantify the functional importance FI of the node; the functional importance NFI of node m m The calculation is as follows: Calculate the NRP importance of each node and select the top 2k nodes with the largest NRP values as another set of candidate nodes.

6. The method for maximizing the influence of information dissemination based on node feature fusion and community detection according to claim 1 is characterized in that: In step 3, during the seed node selection phase, firstly, common nodes in the two sets of candidate nodes (theoretically, a total of 4k candidate nodes) are screened out; (1) If the number of public nodes obtained is exactly equal to k, then this set of public nodes is the final set of seed nodes; (2) If the number of public nodes obtained is less than k, the probability of non-public nodes being selected as seed nodes is calculated, and the top several candidate nodes with the highest probability will be selected as the final required seed nodes until the required number is met; (3) In addition, if the number of public nodes is greater than k, some nodes need to be removed. Specifically, first sort the nodes in the community in descending order according to the number of nodes in the community. Secondly, determine which communities the group of nodes belongs to. If there are more than or equal to 2 nodes in the same community, randomly select a node from the community and leave it. In the end, each community has only less than or equal to 1 public node as a seed node. Then, count the number of seed nodes in all communities. If it is k, the seed node selection ends. If it is less than k, the processing method is the same as the case where the number of public nodes is less than k. The difference is that here we need to count the remaining public nodes. If it is greater than k, remove the node from the minimum community size until the number of nodes meets the requirement.

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