CN115442243A - Time sequence network node centrality evaluation method and device based on time sequence path tree - Google Patents
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Abstract
The application relates to a method and a device for evaluating the centrality of a time sequence network node based on a time sequence path tree, which are used for identifying influential propagators in the time sequence network based on the centrality (SPT-C) index of the time sequence path tree. The SPT-C approach focuses on combining multiple temporal heterogeneity features to speed up and maximize true propagation. Second, the timing Path Tree (SPT) applies a tree structure to limit the number of possible propagation paths between nodes, compresses the specific propagation in the display path flow model, and integrates the potential paths into the shortest paths from the root node to other nodes using a set of contact times, making it simple and fast to extract timing information, improving the efficiency of identifying influential propagators in the timing network.
Description
Technical Field
The present application relates to the field of complex networks and time sequence networks, and in particular, to a method and an apparatus for evaluating the centrality of a time sequence network node based on a time sequence path tree.
Background
Identifying nodes that play an important role in complex networks is a matter of great interest in recent years. As this may help solve many real-world practical problems such as determining "superpropagators" in the spread of infectious diseases, determining key people for information exchange in online social networks, and finding the most influential areas in national product promotions, etc.
Currently, the importance of a single node can be defined from different perspectives, such as the size of infection that can be caused by an infected propagator, the speed at which the node is affected, and the impact of removing nodes on the survivability of the network. On the basis, the related technology provides various centrality indexes. While these metrics have good performance on static networks, they may not be suitable for solving practical problems because static structures do not fully describe true social relationships.
In a real social network, the connections between individuals are intermittent and transient. For example, in Email networks a corresponding connection between users is only made when sending or receiving mail. The dynamics mechanism may use a time-ordered network to better ground search for foxes, which consists of a series of contact events. Therefore, how to effectively identify important nodes (such as influential propagators in the propagation process) in a more real time-series network has received much attention in recent years.
To solve this problem, it is a basis for studying a time series network to construct an efficient time series network representation structure so as to extract time series information. The representation structure in the related art is a displayed path flow model, which extracts a time-series path representing the occurrence of an event between each pair of nodes. The timing path is described as a monotonically increasing sequence of timing stamp edges. By describing the flow path of propagation, the structure is more sensitive to the evolution of the network and achieves impressive performance. However, due to different requirements on the features, the process of extracting the time-series features based on the structure has higher complexity. Thus, there is still much room for improvement in displaying the path flow model.
Disclosure of Invention
The application provides a time sequence network node centrality evaluation method and device based on a time sequence path tree, so as to quantify influences of propagators in a time sequence network. The technical scheme of the application is as follows:
according to a first aspect of an embodiment of the present application, a method for evaluating the centrality of a time sequence network node based on a time sequence path tree is provided, where the method includes:
step 1: taking any node in a time sequence network as a root node, constructing a group of time sequence path trees, wherein the time sequence path trees further comprise non-root nodes, the root node has three time sequence heterogeneous characteristics of propagation time, hop count and reachable path count, the propagation time is used for representing the time spent by the node in the infection propagation process, the hop count is used for representing the number of other nodes needing to be passed in the propagation process, and the reachable path count is used for reflecting the size of potential time sequence path scale from the root node to the non-root node;
step 2: respectively constructing feature matrices of the propagation time, the hop count and the reachable path count, wherein a row vector corresponding to the root node stores time sequence feature values of all target nodes calculated based on the time sequence path tree;
and 3, step 3: normalizing the time sequence characteristic matrix, and calculating the time sequence centrality of each node in the time sequence network based on the normalized time sequence characteristic matrix;
and 4, step 4: and sequencing the nodes in the time sequence network according to a time sequence network node centrality evaluation model based on a time sequence path tree so as to identify influential propagators.
Optionally, the timing path tree includes a plurality of nodes, each node represents a propagator recording timing characteristic information, and each undirected edge indicates that at least one contact between a parent node and a child node has occurred.
Optionally, when a group of the timing path tree is constructed, a first condition and a second condition should be satisfied at the same time, where the first condition is that at least one timing path exists between the root node and any child node, and the second condition is that each timing path in the timing path tree satisfies a shortest time first rule.
Optionally, v i Representing a root node, v, in a time-sequential path tree j Representing non-root nodes in a time-series path tree, the propagation time being defined in particular as a time path
The maximum timestamp on the last edge of the set, the propagation time and the recovery probability are in a direct relationship.
Optionally, the hop count passes through the path
Is calculated, wherein if v is j And v i V is farther away, v j The infection rate decreases exponentially, the less likely the infection is.
Optionally, the reachable path number may be v in a computation timing path tree j The number of contact timestamps with the parent node approaches infinity.
Optionally, the propagating influence
Expressed as:
wherein v is i Representing the root node in the time-sequential network,
representing a tree of time-sequential paths, v j (v j E.g., V) represents a tree of timing paths
A non-root node in (1); omega 0 (ω 0 ∈[0,1])，ω 1 (ω 1 ∈[0,1]) Representing a weight parameter, ω 0 +ω 1 ≤1；
Respectively propagation time
Hop count
And number of reachable paths
The normalized timing characteristics matrix of (a).
Optionally, the normalizing the feature matrix of the propagation time, the hop count, and the reachable path count specifically includes:
wherein R is max And R min Representing the maximum and minimum number of reachable paths between any pair of nodes, respectively.
According to a second aspect of the embodiments of the present application, there is provided a device for evaluating the centrality of a time series network node based on a time series path tree, including: a processor; a memory for storing the processor-executable instructions; wherein the processor is configured to execute the instructions to implement the method for evaluating the centrality of a time-series network node based on a time-series path tree of any one of the methods mentioned in the first aspect.
The technical scheme provided by the embodiment of the application at least has the following beneficial effects:
the invention firstly provides a method and a device for evaluating the centrality of a time sequence network node based on a time sequence path tree, which are used for identifying influential propagators in the time sequence network based on the centrality (SPT-C) index of the time sequence path tree. The SPT-C approach focuses on combining multiple temporal heterogeneity features to speed up and maximize true propagation. Second, SPT applies a tree structure to limit the number of possible propagation paths between nodes, where one non-root node has and only has one parent node. This structure compresses the specific propagation in the display path flow model and uses the set of contact times to integrate the potential path into the shortest path from the root node to other nodes. On this basis, the timing characteristics in propagation will be embodied in the tree depth and node data. The structure ignores some details of the non-shortest path which have little influence on the structure, thereby making it simple and fast to extract the timing information.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the application and are not to be construed as limiting the application.
FIG. 1 is a flow diagram illustrating a method for timing network node centrality assessment based on a timing path tree in accordance with an exemplary embodiment;
FIG. 2 is a schematic diagram illustrating a timing path tree constructed based on node I in accordance with an exemplary embodiment;
FIG. 3 is a schematic diagram illustrating a method for sequential network node centrality assessment based on a sequential path tree in accordance with an exemplary embodiment;
fig. 4 illustrates Pearson correlation coefficients between different centrality-based node rankings and the true ranking based on the SIR model and matching rates at different tops k%, according to an example embodiment.
Detailed Description
In order to make the technical solutions of the present application better understood by those of ordinary skill in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It should be understood that the data so used may be interchanged under appropriate circumstances such that embodiments of the application described herein may be implemented in sequences other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the application, as detailed in the appended claims.
As shown in fig. 1, the present application provides a method for evaluating node centrality of a time series network based on a time series path tree, which can easily identify the centrality of an influential propagator through nodes in a sorted time series network. The method mainly comprises the following four steps:
step 1: taking any node in a time sequence network as a root node, constructing a group of time sequence path trees, wherein the time sequence path trees also comprise non-root nodes, any node in the trees has three time sequence heterogeneous characteristics of propagation time, hop count and reachable path count, the propagation time is used for representing the time spent by the node in the infection propagation process, the hop count is used for representing the number of other nodes needing to be passed through in the propagation process, and the reachable path count is used for reflecting the size of the potential time sequence path scale from the root node to the non-root node.
In some embodiments, each node in the time-series network is taken as a root node v i Constructing a set of time sequence path trees
Wherein any one node v j With propagation time
Hop count
Number of reachable paths
Three sequential isomerism characteristics, v j For non-root nodes, the propagation time
Representing a node v j Time taken for infection transmission process, number of said hops
Representing the number of other nodes that need to be traversed during propagation, the number of reachable paths
For reflecting slave node v i To v j The size of the potential timing path size.
Step 2: and respectively constructing feature matrixes of the propagation time, the hop count and the reachable path count, wherein a row vector corresponding to the root node stores time sequence feature values of all target nodes calculated based on the time sequence path tree.
In some embodiments, the travel times are constructed separately
Hop count
Number of reachable paths
Of T, L and R, where any node v i The corresponding row vector holds a tree based on the time sequence path
And calculating the timing characteristic values of all the target nodes.
And step 3: and normalizing the time sequence characteristic matrix, and calculating the time sequence centrality of each node in the time sequence network based on the normalized time sequence characteristic matrix.
In some embodiments, the time-series feature matrix is based on normalization
And
calculating each node v in the time sequence network i Time sequence centrality of
And 4, step 4: and sequencing the nodes in the time sequence network according to a time sequence network node centrality evaluation model based on the time sequence path tree so as to identify the influential propagators.
In some embodiments, the present application exemplarily proposes a new timing network representation structure, sequential-PathTree (SPT). As shown in fig. 2, the timing path tree is a special type of tree in which each node represents a propagator that records timing characteristic information, and each undirected edge indicates that at least one contact between a parent node and a child node has occurred.
The above described timing network representation structure compresses the specific propagation in the explicit path flow model and integrates the rest of the contact events and set of potential paths into the shortest timing path to satisfy the structural properties of the tree, i.e. the uniqueness of the parent node. Therefore, the constructed timing path tree should satisfy the following two conditions at the same time:
the first condition is that: at least one time sequence path exists between the root node and any child node;
the second condition is that: each time sequence path in the time sequence path tree meets the time shortest priority principle.
According to the above definition, the time sequence path tree
Containing the slave root node v i To start, to any other node v j All timing paths to end
For example, by using a graph traversal algorithm based on the earliest-in-time principle, a time-series network containing 13 nodes can be constructed, as shown in (a) of fig. 2. Constructing a time sequence path Tree based on a root node I I As shown in fig. 2 (B). Tree constructed from (B) of FIG. 2 I In the method, the root node I to any child node (such as P) can be extracted I→D ,P I→M ) Of a set of timing paths other than P I→F (indicating that node I cannot reach node F).
It is noted that in the timing path tree, each timing path is irreversible, i.e. it is not reversible
The weighted neighbor matrix corresponding to the timing path tree is therefore asymmetric. At the same time, in the same timing path tree, the slave node v i To
There may be multiple potential timing paths. Therefore, the shortest timing path based on the fastest propagation time or number of hops is of particular note, which means once v is taken i Is infected, node v i Infection v j The speed of (2).
In some embodiments, on the basis of the constructed time sequence path tree, three time sequence isomerism characteristics considered by the application can be extracted, including propagation time
Hop count
Number of reachable paths
Three timing characteristics are defined as follows:
propagation time: for each node v j The transmission time represents the time taken for the infection transmission process and can be defined as
Maximum time stamp on last edge, e.g. T I→D ＝2，T I→M ＝2，T I→F = ∞. The propagation time affects the probability of recovery of the propagator, and generally the propagation time is in direct proportion to the probability of recovery, and the longer the time taken, the more likely the recovery is, resulting in the breakage of the infection propagation chain. It is worth mentioning that nodes that recover from infection will not be infected any more.
Hop count: the hop count represents the number of other nodes that need to be passed through in the propagation process and can pass through the path
Is calculated as L I→D ＝2，L I→M ＝2，L I→F = ∞. If v is j And v i Is far away, it means v j The infection rate decreases exponentially, the less likely the infection is.
Number of reachable paths: the number of reachable paths reflects the slave node v i To v j The size of the potential timing path size. Computing v in a sequential path tree j Number of contact time stamps with parent node to approximate the number of reachable paths, e.g. R I→D ＝1，R I→M =2 and R I→F ＝0。
In some embodiments, based on the determination of the timing Path Tree, the present application proposes a timing network node Centrality evaluation model (referred to as Sequential-Path Tree-Based center, SPT-C) Based on the timing Path Tree to quantify the influence of the propagator in the timing network. The centrality defines node v i Is its propagation influence in the timing path tree
In particular, the method comprises the following steps of,
wherein v is j (v j E.g., V) represents a tree of timing paths
A non-root node of; omega 0 (ω 0 ∈[0,1])，ω 1 (ω 1 ∈[0,1]) Representing a weight parameter, ω 0 +ω 1 ≤1；
Normalized timing feature matrices for propagation time, hop count, and reachable path count, respectively.
In order to ensure monotonous consistency, the application carries out normalization processing Norm (·) on three characteristic matrixes of propagation time, hop count and reachable path count:
wherein R is max And R min Representing the maximum and minimum number of reachable paths between any pair of nodes, respectively.
In some embodiments, in the time series network node centrality evaluation method based on the time series path tree, it can be easily identified that the influential propagator passes through the node centrality in the ordered time series network, and the whole identification process is performed as algorithm 1, as shown in fig. 3, which also exemplifies a time series network node centrality evaluation method based on the time series path tree of the present application.
In some embodiments, table 1 summarizes the basic statistics of the 12 true time-series networks used by the present application to validate, including the number of nodes, edges, contacts, and total sampling time for each network.
Illustratively, the present application employs a Susceptible-fed-Recovered (SIR) model to simulate an outbreak of an infectious disease, and uses the simulation results to evaluate the effectiveness of SPT-C in identifying the most influential propagators. The SIR model is a propagation model and is an abstract description of the information propagation process. Meanwhile, the SIR model is the most classical model among infectious disease models, where S (separable) represents a Susceptible person, I (infectious) represents an infected person, and R (Removal) represents a removed person. SIR models are applied in the study of information propagation. In the SIR model, the propagation process roughly includes: initially, all nodes are in a susceptible state. Then, after some nodes are contacted with information, the nodes become infected states, and the nodes in the infected states try to infect the nodes in other susceptible states or enter a recovery state. Infecting a node is the attitude to pass information or something. The recovery state, i.e. immunity, the node in the recovery state is no longer involved in the propagation of information. Wherein β represents an infection rate and γ represents a recovery rate.
In a further embodiment, to eliminate the randomness of the simulation based on the SIR model, the importance of each node is calculated by running a certain number (e.g., 2000) and averaging. Meanwhile, the effectiveness of the time sequence centrality in the two aspects of consistency and accuracy is evaluated by using the Pearson correlation coefficient and Top k% as indexes. These two evaluation indices ρ, top k％ Is defined as:
table 1 sequential network architecture features as used herein
In table 1, N represents the number of nodes, E represents the number of edges (edges between two nodes are at least once in contact) in the aggregate static graph, C represents the number of contact events, and T represents the total sampling time.
In some embodiments, the validity of SPT-C is compared to the other 6 reference timing centroids. The aim is to compare the classical and the latest various centrality indexes, making the comparison more convincing. The 6 kinds of reference centralities are respectively a time-series centrality (2012) based on the snapshot, a time-series betweenness centrality (2013) based on the snapshot, a time-series adjacent centrality (2017) based on the time-series path, and three kinds of centrality indexes (2021) based on the time-series gravity model.
The results of the SPT-C comparison with the 6 baseline methods presented in this application are shown in Table 2 and FIG. 4. Table 2 shows Pearson correlation coefficients between each time-series centrality and the node importance calculated by the SIR model, and the bold numerical term represents the time-series centrality measure with the highest correlation. Fig. 4 shows the matching rates of node ranking based on different centralities and true ranking based on SIR model at different Top k%.
In a further embodiment, each weight parameter in the SPT-C method is set to a fixed value, ω 0 ＝0.3，ω 1 =0.1, and assumes that the infection rate and recovery rate in SIR model simulations are also fixed values, β =0.3 and γ =3, respectively.
TABLE 2 Pearson correlation coefficient between temporal centrality and node importance based on SIR model
The comparison result of the two evaluation indexes shows that the SPT-C based on the multi-time sequence isomerism characteristic has better performance in the aspects of measuring the node centrality in the time sequence network and identifying the influential propagator. As shown in table 2, the Person correlation coefficient of SPT-C outperforms the other 6 reference centricity over all 12 true datasets. The bold numerical item means that the matching degree of the calculated node centrality and the real value in the current time sequence network is the highest. FIG. 4 shows that when the Top node percentage is greater than 0.1, the Top k% metric of SPT-C is always better than other reference timing centralities across all timing networks. By observation, the SPT-C can reach a matching rate of more than 25% at a Top of 10%, and reach a matching rate of more than 80% at a Top of 50%.
The application provides a novel node centrality evaluation method based on a time sequence path tree, and each node in a time sequence network is used as a root node v i Constructing a set of time sequence path trees
Each node has three time sequence heterogeneous characteristics of propagation time, hop count and reachable path count; respectively constructing characteristic matrixes T, L and R of propagation time, hop count and reachable path number, wherein any node v i The corresponding row vector holds a tree based on the time sequence path
Calculating time sequence characteristic values of all target nodes; time sequence characteristic matrix based on normalization
And
each node v in the computation time sequence network i Time sequence centrality of
Nodes in the time series network are ordered based on the SPT-C values of the metrics, thereby quickly identifying influential propagators. Under the background of identifying influential propagators, various time sequence heterogeneity characteristics such as propagation time, hop count and reachable path count are comprehensively considered to measure the importance of the nodes. Meanwhile, the application provides a new time sequence network representation structure, namely a time sequence path tree, which is used for extracting time sequence characteristics and calculating centrality. Also shown by evaluation experiments on 12 real time-series networks, SPT-C is in search of the most influential propagatorsMore accurate than the reference timing centrality.
The application relates to a method and a device for evaluating the centrality of a time sequence network node based on a time sequence path tree, which are used for identifying influential propagators in the time sequence network based on the centrality (SPT-C) index of the time sequence path tree. The SPT-C method focuses on combining multiple temporal heterogeneity features to accelerate and maximize true propagation. Second, the timing Path Tree (SPT) applies a tree structure to limit the number of possible propagation paths between nodes, compresses the specific propagation in the display path flow model, and integrates the potential paths into the shortest paths from the root node to other nodes using a set of contact times, making it simple and fast to extract timing information, improving the efficiency of identifying influential propagators in the timing network.
The application scenario described in the embodiment of the present application is for more clearly illustrating the technical solution of the embodiment of the present application, and does not form a limitation on the technical solution provided in the embodiment of the present application, and it can be known by a person skilled in the art that with the occurrence of a new application scenario, the technical solution provided in the embodiment of the present application is also applicable to similar technical problems.
As will be appreciated by one skilled in the art, aspects of the present application may be embodied as a system, method or program product. Accordingly, various aspects of the present application may be embodied in the form of: an entirely hardware embodiment, an entirely software embodiment (including firmware, microcode, etc.) or an embodiment combining hardware and software aspects that may all generally be referred to herein as a "circuit," module "or" system.
In some possible implementations, an electronic device according to the present application may include at least one processor, and at least one memory. Wherein the memory stores program code which, when executed by the processor, causes the processor to perform the operational data management method according to various exemplary embodiments of the present application described above in this specification. For example, the processor may perform steps as in an operational data management method.
Further, according to the apparatus for evaluating the centrality of a time-series network node based on a time-series path tree of this embodiment of the present application, the steps in the method for evaluating the centrality of a time-series network node based on a time-series path tree mentioned in the above embodiment may be performed.
In an exemplary embodiment, various aspects of a timing network node centrality assessment method and apparatus based on a timing path tree provided by the present application may also be implemented in the form of a program product, which includes program code for causing a computer device to perform the steps in the method for maximizing quality of experience in a multi-antenna drone video transmission system according to various exemplary embodiments of the present application described above in this specification when the program product is run on the computer device.
It should be noted that although several units or sub-units of the apparatus are mentioned in the above detailed description, such division is merely exemplary and not mandatory. Indeed, the features and functions of two or more units described above may be embodied in one unit, according to embodiments of the application. Conversely, the features and functions of one unit described above may be further divided into embodiments by a plurality of units.
Further, while the operations of the methods of the present application are depicted in the drawings in a particular order, this does not require or imply that these operations must be performed in this particular order, or that all of the illustrated operations must be performed, to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable image scaling apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable image scaling apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable image scaling apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable image scaling device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer implemented process such that the instructions which execute on the computer or other programmable device provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the preferred embodiments of the present application have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all alterations and modifications as fall within the scope of the application.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
Claims (9)
1. A time sequence network node centrality evaluation method based on a time sequence path tree is characterized by comprising the following steps:
step 1: taking any node in a time sequence network as a root node, constructing a group of time sequence path trees, wherein the time sequence path trees further comprise non-root nodes, the root node has three time sequence heterogeneous characteristics of propagation time, hop count and reachable path count, the propagation time is used for representing the time spent by the node in the infection propagation process, the hop count is used for representing the number of other nodes needing to be passed in the propagation process, and the reachable path count is used for reflecting the size of potential time sequence path scale from the root node to the non-root node;
step 2: respectively constructing feature matrices of the propagation time, the hop count and the reachable path count, wherein a row vector corresponding to the root node stores time sequence feature values of all target nodes calculated based on the time sequence path tree;
and step 3: normalizing the time sequence characteristic matrix, and calculating the time sequence centrality of each node in the time sequence network based on the normalized time sequence characteristic matrix;
and 4, step 4: and sequencing the nodes in the time sequence network according to a time sequence network node centrality evaluation model based on the time sequence path tree so as to identify the influential propagators.
2. The method of claim 1, wherein the timing path tree comprises a plurality of nodes, each node representing a propagator that records timing characteristics information, each undirected edge indicating at least one contact between a parent node and a child node.
3. The method of claim 2, wherein a first condition and a second condition are simultaneously satisfied when constructing a group of the timing path tree, the first condition is that at least one timing path exists between a root node and any child node, and the second condition is that each timing path in the timing path tree satisfies a shortest time first rule.
4. The method of claim 3, wherein v is i Representing a root node, v, in a time-sequential path tree j Representing non-root nodes in a time-series path tree, the propagation time being defined in particular as a time path
The maximum timestamp on the last edge of the set, the propagation time and the recovery probability are in a direct relationship.
5. The method of claim 4, wherein the hop count is via a path
Is calculated, wherein if v is j And v i V is farther away, v j The infection rate decreases exponentially, the less likely the infection is.
6. The method of claim 5, wherein the reachable path number is v in a computation timing path tree j The number of contact timestamps with the parent node approaches infinity.
7. The method of claim 6, wherein the propagating influence is
Expressed as:
wherein v is i Representing the root node in the time-series network,
representing a tree of time-sequential paths, v j (v j E.g., V) represents a tree of timing paths
A non-root node of; omega 0 (ω 0 ∈[0,1])，ω 1 (ω 1 ∈[0,1]) Representing a weight parameter, ω 0 +ω 1 ≤1；
Respectively propagation time
Hop count
And number of reachable paths
The normalized timing characteristics matrix of (1).
8. The method according to claim 7, wherein normalizing the feature matrices of the propagation time, the hop count, and the reachable path count specifically comprises:
wherein R is max And R min Representing the maximum and minimum number of reachable paths between any pair of nodes, respectively.
9. An apparatus for evaluating the centrality of a time-series network node based on a time-series path tree, comprising:
a processor;
a memory for storing the processor-executable instructions;
wherein the processor is configured to execute the instructions to implement the method of sequential path tree based sequential network node centrality assessment according to any one of claims 1 to 8.
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