Identifying Key Node with Motif-Based PageRank on Acupoint-Disease Network

Existing research combines acupuncture theory with network science and proposes a new paradigm for the study of acupoint selection patterns—a key acupoint mining algorithm based on acupoint networks. However, the basic idea of this study for finding key acupoints is based on binary acupoint synergy relationships, which ignores the higher-order synergy among multiple acupoints and does not truly reflect the implicit patterns of each acupoint among meridian systems. Moreover, the mining results assessment method, which this new paradigm involves, does not have wide applicability and universality. In this paper, with the introduction of higher-order interactions between multiple acupoints, a high-specificity key acupoint mining algorithm based on 3-node motif is proposed in the acupoint-disease network (ADN). In response to the narrow applicability of the new research paradigm involving the evaluation of algorithms' measures, new and widely applicable and universal evaluation criteria are introduced in terms of resolution, network loss, and accuracy, respectively. Based on the principles of acupoint selection involved in acupuncture clinics in Chinese medicine, the acupoints involved in the data were divided into a total of 19 regions according to their distribution characteristics. From these 19 regions, we selected the key acupoints that have a large impact on the global network. Finally, we compared this algorithm with five other acupoint importance assessment algorithms in terms of resolution, network loss, and accuracy, respectively. The comprehensive results show that the algorithm identifies key acupoints with an accuracy of 63%, which is 14% to 21% higher than other existing methods. The key acupoints identified by the algorithm have a significant disruptive effect on the connectivity of the network, indicating that the key acupoints are at the core of the acupoint-disease network topology. They have a significant propagation influence on other acupoints, which means that the key acupoints have high-synergistic cooperation with other acupoints. Meanwhile, the stability and specificity of the algorithm ensure the reliability of the key acupoints. We believe that the key acupoints identified by the algorithm can be used as core acupoints from the perspective of network topology and high synergy of other acupoints, respectively, and help researchers explore targeted and high-impact combinations of acupoints to optimize existing acupuncture prescriptions under condition constraints.


Introduction
As a traditional medical method, acupuncture has important medical value and reliable clinical efcacy and has been recognized by many international organizations [1].In traditional Chinese medicine (TCM), acupuncture is a method in which the TCM doctor selects the appropriate acupoints along the afected meridians for the disease and solves the clinical problem through needling, pressure, or thermal stimulation.With the rapid development of modern medicine, a large number of scholars have launched an exploration of the potential medical value of the meridian system, the mechanisms of interaction with other organs, and the full range of information about acupoints [2][3][4][5].In addition, researchers have summarized the common acupoints and selection patterns for specifc diseases based on historical treatment case data [6][7][8][9].Scholars in other felds have also studied the characteristics of acupoint selection for treatment of diseases using the bioelectric potential of acupoints and their standard errors [10].
Te human meridian system is a network of interwoven meridians and collaterals.It forms a complex structural and functional system along with other systems of the body.Meridians are scattered throughout the body and interact with other subsystems to transmit and regulate the physiological information of the body.Tis coincides with the idea of network science.Te use of complex network thinking to explore the laws of acupoint selection has become a new trend in TCM research, where the identifcation of key nodes in complex network analysis methods can support new insights into the study of acupoint-disease relationships.Tere has been much literature on the preliminary application of complex network theory to the study of acupoint-disease relationships [11,12].On this basis, there is also the use of complex networks to study the combination pattern of acupuncture points for diferent diseases [13][14][15][16][17][18].Te characteristics of the above literature are shown in Table 1.
However, most of the aforementioned literature uses network-based statistical analysis to study combinations of acupoints, but has not yet gone further to use network thinking to analyze the relationship between acupoints and diseases and to dig deeper into the information contained in the network.Shi et al. [19] investigated a new method of supplementary acupoint selection with in-depth reference to complex network theory.Tis research work constructed a weighted undirected acupoint-disease network (ADN) based on clinical acupuncture prescription literature.Based on ADN, the key node identifcation method is used and three evaluation metrics (resolution, network loss, and accuracy) are introduced to select key points for each meridian.Among them, resolution measures the ability of the algorithm to distinguish the size of the efect produced by the acupoints in a specifc region or at a specifc range.Network loss measures the ability of the key acupoints identifed by the algorithm to transfer physiological information between the target regions.Accuracy measures the ability of the key acupoints mined by the algorithm to produce a synergistic size with other acupoints.Under these three metrics, higher scores indicate that the algorithm is stronger in the corresponding ability and vice versa.
From the perspective of clinical acupuncture in TCM, this new research idea has more far-reaching implications.First, exploring key acupoints from ADN can be understood as analyzing the abstract distance between acupoints from a large amount of clinical prescription data.Second, it helps to understand the macroscopic connections between acupoints from the perspective of symptoms.
Networks proposed in the aforementioned literature are obtained based on the idea of constructing binary relationships that express the interactions between nodes in their most simplifed form.For example, the network was constructed from clinical acupuncture prescription data based on the principle that two acupoints act on at least one disease.However, the binary relationship ignores more information about multiple interactions.
Tat is, the key nodes obtained from the above literature are not synergistic with other nodes and have a strong isolation, which may be inefective if such acupoints are used in conjunction with other acupoints to treat a disease.In clinical acupuncture prescriptions, multiple acupoints act simultaneously on a disease, i.e., multiple acupoints produce higher-order interactions.Tis higher-order interaction indicates that multiple acupoints simultaneously regulate physiological information in the body.Obviously, such higher-order interactions cannot be ignored.Accordingly, key acupoint mining algorithms that ignore such higherorder interactions can lead to inaccurate key acupoints obtained.Te higher-order interactions of multiple acupoints can refect not only the cooperative ability of multiple acupoints but also the potential connections between multiple acupoints.Mining higher-order interactions between multiple acupoints can lead to potential combinations of acupoints with high-synergistic ability.At the same time, the resolution, network loss, and accuracy introduced in [19] have a narrow applicability and are not able to evaluate and refect the higher-order interaction ability between nodes.
In this paper, based on the above description, the motifbased PageRank (MPR) algorithm is proposed based on the research work of [19].Te algorithm is based on the ADN, which reconstructs the weights of the network edges by measuring the amount of synergistic information in each triplet to obtain a new synergy matrix.Using the background knowledge of Chinese medicine, the ADN is divided into 19 regions.Ten, the PageRank algorithm was used to fnd the key acupoints for each region.In brief, the contributions of this work are summarized as follows: (i) In response to the binary relationship that would ignore the multivariate interaction information, a higher-order interaction of multiple acupoints is introduced in the ADN network, and the interaction is expressed in the form of a 3-node modulus.(ii) Due to the introduction of higher-order interactions, the conventional adjacency weight matrix cannot express higher-order interactions.Terefore, we reconstructed the adjacency weight matrix of the binary relationship network to obtain a synergistic strength matrix containing multiple synergistic relationships.Ten, the PageRank algorithm was used to fnd the key points for each region.(iii) Te network loss and accuracy calculation methods introduced in [19] cannot measure the goodness of key acupoint mining algorithms with higher-order interactions, so we introduce new and widely applicable calculation methods.

Data Availability.
Te data source used in this paper consists of two parts.Te frst part was selected from the 1994 acupuncture prescriptions for 50 common conditions used in [19,20], which is a summary of the acupuncture point selection for 50 common conditions To indicate that the key point mining algorithm is not dependent on a specifc dataset, the most recent acupuncture literature data was chosen for the second part.Te changes of major acupoints in ancient and modern acupuncture treatments over time were explored in [21], which involved modern acupuncture treatment literature from the CDSR (Cochrane Database of Systematic Reviews) with high authority.Terefore, we chose CDSR as the primary source of data for the modern acupuncture treatment literature.

Data Cleaning and Extraction.
Te frst part of the dataset records the relationship between the disease and the corresponding acupoint set, so it can be collected directly using key-value pairs, where the disease is the keyword and the acupoint set is the corresponding value.
For the second part of the dataset, the process described in Figure 1 is used for collection, as shown in Figure 1.Since these two datasets cannot guarantee the unbiasedness of the dataset itself, in order to be able to include more special cases and considering more cases, we merged these two datasets into one dataset to provide data support for the subsequent work.

Acupoint-Disease Network (ADN).
Te key-value pairs in the data formally describe the synergistic therapeutic efect of multiple acupoints on the disease, which implies the association relationship between the acupoints.In this paper, we use the ADN network proposed in [19], which is an acupoint association network obtained from the construction of acupoints based on the synergistic efect of the acupoint set on the disease.Te formal representation of the network is specifed as follows: Te key-value pairs in the data formally describe the synergistic therapeutic efect of multiple acupoints in the acupoint set on the disease, which implies the association relationship between the acupoints.In this paper, we used the ADN from [19], which uses acupoints as nodes and establishes a link between any two nodes when they appear in one disease at the same time, with the number of disease types that appear as the weight of that edge.Te formal representation of the network is specifed as follows: where V denotes the set of acupoint nodes of the network, i.e., the set of acupoints.E denotes the set of edges of the network, i.e., the set of association relationships between acupoints.If two acupoints act on one disease at the same time, an association relationship is established between these two acupoints.If two acupoints act on more than one disease, the strength of the association between these two Network analysis [6] Traditional controlled experiments ✓ [7] Traditional controlled experiments ✓ [8] Traditional controlled experiments ✓ [9] Historical case analysis ✓ [12] Analysis of complex networks ✓ ✓ [13] Analysis of complex networks ✓ ✓ [14] Analysis of complex networks ✓ [15] Analysis of complex networks ✓ [16] Analysis of complex networks ✓ [17] Analysis of complex networks ✓ [18] Analysis of complex networks ✓ [19] Analysis of complex networks ✓ ✓ Raw dataset acquisition: we searched the CDSR using the keyword "acupuncture" and obtained all the corresponding literature.
Filter ineligible data: Keep data entries that contain data on the use of acupoints to treat diseases in the paper Extraction of diseases and corresponding therapeutic acupuncture points: using manual reading method to extract the relationship between diseases and acupoints in corresponding data entries Available dataset acquisition: we store the extracted disease and acupoint relationships, with diseases as keywords and acupoint sets as values, as CSV fles for subsequent construction of ADN Evidence-Based Complementary and Alternative Medicine acupoints is expressed in the form of weights, where W(E) denotes the weight distribution of the association relationship between the acupoints.Figure 2 shows the ADN network constructed from the data in this paper.First, using the "NetworkX" package in the Python programming language, a link is established between any two acupuncture points when they act on a disease at the same time.Te number of diseases that the connection acts on is used as the weight of the connection.Second, a graph fle is generated using the Python programming language and visualized using Gephi software.We analyzed the ADN in terms of attributes such as network degree distribution, average degree, average weighted discard, and network clustering coefcient.Te results of network analysis are shown in Table 2.
Figure 3 depicts the node degree distribution of the ADN.As can be seen in Figure 3, the degree distribution exhibits a small-world network characteristic, which is extremely close to the normal distribution (shown by the ftted line in the fgure).Te large number of node degrees in the network tends to be in the peak of the distribution curve, indicating that the node degrees in the network are not widely disparate.Similarly, this phenomenon can be seen in the properties of the network, as shown in Table 2.
Te average clustering coefcient of the network describes the degree of close association between acupoints, and the average weighted degree describes the frequency of use of each acupoint.As seen in Table 2, the ADN has a high average clustering coefcient and average weighting, indicating that the acupoints are closely related to each other  Evidence-Based Complementary and Alternative Medicine and that each acupoint is used more frequently.Tat is, the algorithm cannot distinguish the key acupoints on each meridian by these attributes alone, and it cannot help TCM doctors to fnd the best combination of acupoints for a specifc disease with limited resources.

Problem Formulation
2.4.1.Motif Defnition.Since multiple acupoints produce synergistic efects in treating diseases, such synergistic efects cannot be expressed completely by pairwise relationships only, which will produce loss of information.Terefore, previous key acupoint mining algorithms established based on pairwise relationships loses the accuracy of key acupoints selected on each meridian.We used theoretically mature network motifs in complex networks for the description of multipoint synergy, on the basis of which the corresponding key acupoint mining algorithm was investigated.Since the description of multiacupoint synergy is too complex, we use 3-node motifs for the description in order to facilitate the abstraction of such a relationship [22].
Defnition 2. M denotes the motif defned on k nodes.A motif M is defned on k nodes by a tuple (B, A), where B is a k × k binary matrix, and A ⊂ 1, 2, . . ., k { } specifes the anchor set, which is the set of the indices of the anchor nodes.
According to Defnition 2, we give a toy model to explain the meaning of the motif.
An example of a 3-node simple motif is given in Figure 4. Te weighted edges connected between nodes indicate multiple simultaneous occurrences of two nodes in the disease treatment prescription, where 1 indicates the number of occurrences and 0 indicates that there are no edges between the nodes.Te orange surface indicates the synergistic relationship of these three nodes, and the geometric area of this triangle indicates the potential synergistic strength of these three nodes.Te B matrix in Figure 4 is the mathematical form representation of the corresponding motif, and A is the node anchor set.

Potential Synergistic Strength Distribution.
We extracted all the 3-node motifs in the ADN and calculated the distribution of synergy strengths of these motifs, and the results show that the synergy strengths of 3-node motifs in the network have the characteristics of power-law distribution, which means that these synergy strengths are signifcantly diferent.To characterize the power-law distribution, we use a double logarithmic coordinate system to demonstrate the potential synergy distribution of the network, as shown in Figure 5.
In Figure 5, the horizontal coordinate indicates the magnitude of synergy strength and the vertical coordinate indicates the probability index of synergy strength.As can be  Evidence-Based Complementary and Alternative Medicine seen, the smaller the strength of the acupoint synergy, the greater the probability of its occurrence in the network and vice versa.With such a clear synergistic relationship of strength, the key acupoints on the meridians can be identifed more accurately.Te algorithm of key acupoint node mining based on synergistic relationship is given.

Key Acupoint Node Mining Based on Synergistic Relationship.
A key node is a special node that plays an important role in a network.Since the propagation, synchronization, and control of physiological information by acupoints cannot be determined from the perspective of modern medicine, the highly abstract complex network model provides us with an efective basis for exploring key acupoints by describing the linking relationships among acupoints.In this work, we combine the ADN network with the actual fourteen meridian distributions and odd point distribution features and propose a key point mining algorithm that satisfes the fourteen meridian distributions and extrameridian point distribution features.In this paper, we continue to follow the defnition of key acupoints in the literature [19], i.e., key acupoints are the acupoint indicated as the core has a wide spatial distribution of indications in acupoint network or the prescription.In a general way, the key acupoint mining algorithm consists of three main steps.First, acupoint clusters are divided according to meridian distribution features.Second, based on the ADN, the characteristics of the nodes in each cluster are extracted and then the importance of the nodes is evaluated.Finally, according to the key node evaluation index, the top 3 key acupoints nodes in each cluster are selected.Based on these steps, we designed a new node evaluation algorithm, the MPR algorithm, and selected a more convincing algorithm performance evaluation index.

Acupoint Communities in the Meridian System.
Due to the "selection of acupoints along the afected meridian" principle, diferent acupoints on the same meridian have a wide range of functions; more obviously, acupoints  Evidence-Based Complementary and Alternative Medicine on certain meridians have the ability to modulate multiple symptoms locally.Tis makes it easy for the algorithm to focus the key acupoints on certain characteristic meridians.Terefore, we divide these acupoints based on the meridian system so that important acupoints with specifc therapeutic efects can be highlighted in the network model and also balance the contribution of each community node to the network, helping TCM doctors to always have key acupoints as references in each target meridian.
Tere are 14 major meridians in the human body, which are the Shaoyin Heart Channel of Hand, the Taiyang Small Intestine Channel of Hand, the Taiyang Bladder Channel of Foot, the Shaoyin Kidney Channel of Foot, the Jueyin Pericardium Channel of Hand, the Shaoyang Sanjiao Channel of Hand, the Shaoyang Gallbladder Channel of Foot, the Jueyin Liver Channel of Foot, the Governing Vessel, and the Conception Vessel.Most of the body's acupoints are located on these 14 meridians.In addition to these acupoints, many extrameridian points are scattered on the surface of the body.Te TCM doctor selects the targeted extrameridian acupoints according to the principles of proximal and symptomatic selection of acupuncture points in the area where the disease occurs.In Chinese medicine, extrameridian acupoints are classifed as Points of Head and Neck, Points of Chest and Abdomen, Points of Back, Points of Upper Extremities, and Points of Lower Extremities.In summary, the nodes in the ADN network were divided into 19 communities, including 14 meridian communities and 5 extrameridian acupoints communities.

Motif-Based PageRank (MPR)
Algorithm.First, we calculated the synergistic strength measurement of threenode motifs.In order to fnd the synergistic strength of each three-node motif, we make use of the efective information (EI) [23], which is a network measure that quantifes the volume of path information between acupoints in a network, as well as how that volume is distributed.Now, we give an equation for calculating the synergy strength of a network G as shown in the following equation: where H(X) � −  x P(x)log P(x).Te frst is the entropy of the average out-weight vector in the network, 〈W out i 〉, which captures how distributed synergistic out-weights between acupoints in the network are.Te second is the average entropy of each acupoint's W out i .Since the ADN contains all the information of the node, the synergistic strength of the 3-node motifs that needs to be measured can be measured by removing the motifs from the ADN.Terefore, the synergistic strength of the 3-node motifs is calculated as shown in equation (3).Defnition 3. EI(∆ i ) represents the synergistic strength of the i-th motifs.
where the ADN with motif ∆ i removed is denoted as Second, the synergy strength matrix H is given.Te synergistic strength of all 3-node motifs in the network is obtained by equation (3).To better portray the importance of nodes, we used the well-established PageRank algorithm to calculate the importance of nodes.However, the algorithm still does not include synergy beyond pairwise relationships and only uses the binary relationship adjacency weight matrix of the network.Since the multinode synergy efect changes the actual strength of interactions between pairs of nodes.Terefore, we can convert the synergy strength of the 3-node motifs between two nodes to obtain a synergy strength matrix with a completely new one, replacing the adjacency weight matrix of the original network.Since paired nodes will appear in diferent 3node motifs, we defne the synergy strength of paired nodes based on 3-node motifs as the weights of the edges between nodes, as shown in the following equation: Figure 6 shows the pairwise relationship adjacency matrix compared with the synergistic strength matrix.Te traditional adjacency weight matrix, as shown in Figure 6(a), can be regarded as the synergy strength matrix of paired nodes.For synergy with more than 2 nodes, the traditional adjacency weight matrix cannot portray such synergy, which will lose a lot of useful information, such that the accuracy of the measured node importance is not high.Figure 6(b) shows the synergy strength matrix of the 3-node motifs, and the orange triangles are marked with the synergy strength of the corresponding motifs.Compared with the traditional adjacency weight matrix, the synergistic strength matrix obtained by equation ( 8) can more efectively utilize the synergistic information of multiple nodes to accurately capture the implied connections between nodes and accurately identify the importance of nodes.For example, the traditional adjacency weight matrix only captures the synergistic relationship between nodes D and B, while synergistic strength matrix based on the 3-node motifs can capture the synergistic relationship between nodes A, B, and D.Moreover, if the importance of nodes is discerned by their weighted degree (summing over the rows or columns of the matrix), the traditional adjacency weight matrix cannot distinguish the importance of nodes A and B and the importance of nodes C and E. In contrast, the importance of these fve nodes can be accurately distinguished by the synergistic strength matrix shown in Figure 6(b).
Tird, node importance is calculated by PageRank.PageRank was originally intended to calculate the importance of each web page under a given network formed by web pages in the Internet world and is widely used today [24].However, in a general sense, PageRank refects the reachability of other nodes to node v i from a topological perspective by means of iterative computation.In [25], a simple iterative algorithm is used to compute the PageRank vector.
Evidence-Based Complementary and Alternative Medicine where x → t is the PageRank vector in step t, x i is the PageRank value of the i-th node in G, and N is the number of nodes.e → ∈ R N is a vector with every entry equal to 1. P is the transition probability matrix obtained by where W is the weighted adjacency matrix of the graph and W ij represents the weight of e ij .For a directed unweighted graph, W ij � 1 if e ij exists and W ij � 0 otherwise.In [26], Bianchini et al. demonstrated that this iterative computation always converges, thus we obtain the PageRank value for each node in the graph.
In an unweighted undirected network, the more reachable paths to node v i , the larger its PR value; while in a weighted undirected network, the higher the weight of reachable paths to node v i , the larger its PR value.At the same time, from the perspective of synergy strength, the higher the PR value of a node, the higher the PR value of its neighbors will be infuenced to some extent.Terefore, no matter original or weighted PageRank, the weights are calculated based on the direct relations between two nodes.In other words, they only consider the binary relations, while ignoring higher-order relations captured by motifs.
Given a network G, the PageRank value of each node represents infuence or importance.W ij represents the strength of relationship between node v i and v j .From equation ( 5), we can see that W afects the transition probability matrix P, thus the fnal PageRank values.Tat is, by changing the matrix W, PageRank is able to capture the information hidden in the network.In summary, the adjacency matrix H, which contains multibody synergy, can provide more information than the matrix W, enabling PageRank to obtain the key nodes with potential maximum synergy strength with multiple nodes.Terefore, we replace the transfer probability matrix P in equation (5) with P H (P ij � H ij / j H ij ).Te importance of nodes in the ADN network is calculated by the improved PageRank algorithm, which is called Motifs-based Pag-eRank algorithm (MPR).

Experimental Environments.
Te software used in this paper is shown in Table 3. Python, with its simplicity, ease of reading, and scalability, is the tool of choice for many researchers working with data.NetworkX is a package that is often used in Python for working with graph type data.Gephi is also commonly used by many researchers to visualize graphs.

Key Acupoint Node in Communities.
In the analysis of the literature [19], it was shown that the disparity in the importance of the key acupoints calculated by the CC algorithm for each community is not signifcant, which indicates that the average distance from all nodes to other nodes is similar in the network topology.It further indicates that in addition to the truly important key acupoints that are selected when tuning local and global physiological information, many acupoints that are related but do not actually play an important role are also selected.Tis is actually due to the fact that the algorithm considers only the local binary relational topological information of the nodes, allowing all nodes to exhibit such similar results.Te results of our proposed MPR algorithm compared with the CC algorithm for the selected key acupoints in each community are shown in Table 4.Among them, there are 14 communities with the same results and 5 communities with diferent results.Due to the limited amount of data, the number of nodes in some communities is less than 3.By comparing the results, our proposed algorithm makes it possible that the acupoints involved in the synergistic interaction of multiple nodes will be ranked higher, making them key acupoints and providing an accurate and valid reference object for TCM doctors.

Performance Evaluation.
In order to verify the reliability of the key acupoints selected by MPR, three metrics, namely, resolution, network efciency, and accuracy, will be used to evaluate the reliability of MPR, respectively.Meanwhile, a comparison experiment with six node importance evaluation metrics is conducted to verify the reliability of MPR.Tese importance evaluation metrics include closeness centrality (CC), betweenness centrality (BC), eigenvector centrality (EC), CLD algorithm [27], and key node algorithm [19].Te closeness centrality considers the reciprocal of the average shortest path distance to u over all n − 1 reachable nodes, which indicates that the higher the closeness centrality of u, the closer the other nodes are to u. Betweenness centrality considers the sum of the fraction of all-pairs shortest paths that pass through u, which indicates that the higher the betweenness centrality of u, the closer it is to the center of the network.Te eigenvector

Resolution.
Resolution is one of the common measures of algorithm performance and refects the extent to which algorithms are able to distinguish acupoints with high similarity in the network [19].We used the benchmark comparison algorithm with MPR to score the 197 acupoints involved in the data and compared the resolution of each algorithm.Resolution was calculated as shown in the following equation: where r A denotes the ranking result of the algorithm, N denotes the number of nodes in the network, R denotes the granularity of the ranking result, and N i denotes the number of i-th nodes in the ranking result.When R � 1, f(r A ) � 0 indicates that the ranking result cannot distinguish the importance of nodes in the network.Te closer the f(r A ) of the algorithm is to 1, the fner the granularity of the sorting result of the algorithm.

Network Efciency.
We believe that key points, as important entry points for regulating local and systemic physiological states, can ensure a large, stable, and accurate transmission of physiological information between target regions, in other words, each key acupoint plays a "bridge" role in the overall network topology.Network efciency measures the bridge role of nodes in the network in terms of shortest paths, i.e., the number of shortest paths through a node.Te higher the number of shortest paths through a node, the greater the bridging role of the node, and vice versa.Te network efciency is calculated by removing the identifed critical nodes of each algorithm comparing the strengths and weaknesses of each algorithm in terms of network efciency [28][29][30].Te network efciency was calculated as shown in equation (7).Te lower the network efciency of the algorithm, the higher the central role of the key acupoints identifed by the algorithm.
3.3.3.Accuracy.In order to measure the accuracy of the key acupoints identifed by the algorithm, a set of benchmark scores is needed.We chose a node capability assessment method for weighted networks, the weighted cascades (WC) model [31][32][33], to calculate the base synergistic capability of all nodes as a benchmark score.Te accuracy of the set of key acupoints identifed by each algorithm is evaluated by measuring the Kendall correlation coefcient between the benchmark scores and the node importance results calculated by each algorithm.Te higher the correlation, the more accurate the node importance ranking results.Te Kendall correlation coefcient is calculated as shown in the following equation: Since key acupoints are able to regulate physiological information throughout the body and locally, they are able to transmit physiological information between diferent regions in a large, stable, and accurate manner, which Evidence-Based Complementary and Alternative Medicine coincides with the basic idea of the WC model.Te WC model measures the synergistic ability of nodes with other nodes from the perspective of information difusion.Because of its high applicability, the model has been widely applied by scholars as a benchmark method to measure the importance of nodes.In this model, the network is frst converted into a directed network, and the difusion probability between nodes is set by the calculation method shown in the following equation: Te importance of each node is measured through the process of information dissemination on the ADN.To facilitate understanding, we use a toy example to demonstrate how this benchmark evaluation criteria work.
Figure 7 illustrates the computational process of WC model.First, the network is transformed into a directed network (undirected edges and converted into bidirectional edges).Second, the weights of the edges of each node pointing to its neighbors are converted into propagation probabilities according to equation (9).Finally, on such a network, the WC propagation process is simulated.Te number of other nodes that each node afects directly and indirectly is obtained as the importance of that node.

Experimental Results
(1) Resolution.We compare the advantages and disadvantages of MPR and the fve benchmark algorithms in terms of resolution by plotting the complementary cumulative distribution function (CCDF) curves.
As can be seen in Figure 8, the resolution of MPR is signifcantly better than the other fve comparison algorithms, indicating that MPR has a more prominent advantage in resolution than the other fve comparison algorithms.MPR utilizes the synergy of multiple nodes, which allows it to distinguish the synergistic ability of each acupuncture point involved in the data with other acupuncture points.In contrast, the other algorithms only use network topological information based on the pairwise relationships and have little ability to distinguish the synergy of acupoints with other acupoints, thus highlighting the importance of synergistic interactions of multiple nodes.
(2) Network efciency.By calculating the network efciency for each algorithm, the results are displayed in Table 5.From the results in Table 5, we can see that the worst network efciency is the CC algorithm, while the best network effciency is the MPR algorithm.From the perspective of network efciency, the key acupoints identifed by MPR play the role of "bridge" in the whole network topology.
(3) Accuracy.Since evaluating the results in this way is probabilistic, we repeated the propagation process 10 times and averaged the obtained results so that their experimental results do not have traces of artifcial selection.We show the Kendall coefcients of each algorithm with respect to the benchmark results in Table 6.As can be seen in Table 6, the accuracy of the MPR algorithm far exceeds that of the other key point evaluation algorithms.Tis highlights the importance of the synergistic efect of multiple acupuncture points.
3.4.2.Discussion.Network science, as a way of thinking that can explain potentially complex phenomena, provides a new perspective for understanding the role of acupoints in the meridian system in the association, transmission, control, and coordination of physiological information.To better explore the key acupoints in ADN, we improved our previous work [19].We designed a new key acupoint mining algorithm based on the higher-order interactions of multiple nodes.Te method far outperformed other key acupoint mining algorithms in the evaluation experiments with three diferent parameters.Te MPR algorithm is able to mine not only the key acupoints on the fourteen meridians of the human body but also extrameridian points on diferent body parts.Using this feature, the TCM doctor can select the acupoints that have the greatest synergistic efect on the target meridians after diagnosis.Although the TCM doctor's acupuncture prescription may vary depending on previous experience, these key acupoints always play a central role.Tese points can be used as preferred acupoints for a variety of selection tools, providing a broader range of physiological modulation and a wider range of possible allocation patterns.Te goal of our work is the same as that done previously [19], to accurately mark key acupoints to optimize and refne acupuncture prescriptions for TCM doctors for common symptoms.
Currently, network science has well-established research results.However, the networks underlying these theoretical results provide only a limited description of the real world, because such network models are constructed from pairwise interactions.In many biological, physical, and social systems, the basic elements of the network interact in groups, and such interactions do not always decompose into pairwise relational couplings.For example, evidence in neural systems suggests that higher-order infuences are statistically   Evidence-Based Complementary and Alternative Medicine and topologically present and important.Similarly, the acupoints chosen by the TCM doctor to treat a disease are synergistic at the same time.Te concept of higher-order interactions is well known in many-body physics, such as strong interactions [34,35] or van der Waals interactions [35], as well as statistical mechanics [36].Several researches have shown that the presence of higher-order interactions can have a signifcant impact on the dynamics of networked systems, from difusion [37,38] and synchronization [39,40] to social [41][42][43] and evolutionary processes [44].
A key acupoint mining algorithm based on higher-order interactions between acupoints can identify key acupoints with high-synergistic efects.In the human meridian system, the higher-order interactions between acupoints cannot be ignored.From the clinical perspective of acupuncture in Chinese medicine, a group of acupoints act together to regulate local and global physiological information for the purpose of healing.However, in previous studies of key acupoints, researchers' models were constructed based on pairwise relationships, ignoring higher-order interactions between acupoints.As a result, the models are not able to capture the more important and substantial information, making the accuracy and applicability of the results sufer considerably.In other words, higher-order interactions can reveal the functions and mechanisms of multiple acupoints in synergy, further explore new combinations of acupoints, and also reveal the robustness of the human meridian system.In general, a specifc acupoint is selected for a specifc disease and that acupoint has specifc disease characteristics.However, it has been demonstrated in the literature [45] that the selection of an acupoint for a specifc disease does not imply that the acupoint has a specifc indication for that disease.In other words, there is not a one-to-one correspondence between disease and acupoint.Te ADN network constructed by the disease-acupoint relationship implicitly expresses the relationship between acupoints at the representation level.Terefore, the key acupoints identifed by the algorithm can help researchers to identify the best acupoint prescriptions faster and more accurately when analyzing local symptoms.
From the perspective of network, key acupoints have a central position in the network and deeply infuence the network connectivity, acupoint synergy strength and network information difusion.Te key acupoint mining algorithm based on higher-order interactions captures not only the path information of the network but also the synergy information between multiple acupoints, which can  Evidence-Based Complementary and Alternative Medicine accurately evaluate each acupoint its infuence in the network and distinguish the importance of each acupoint.In addition, the MPR algorithm uses a new synergistic strength matrix based on the 3-node motifs, so that the edge weights of the network are expressed as the cumulative synergistic strength of the multiple modalities in which the edge is located.Based on this, the higher-order interactions of multiple acupoints allow the acupoints to obtain diferent weight gains of higher-order interactions as a way to increase their value in the network.Acupoints with higher weighting gains have greater disease regulation ability with more Acupoint combination patterns.Tat is, from the perspective of higher-order interactions of acupoints, key acupoint nodes can be used as core acupoints with other acupoints to modulate local physiological states and help researchers explore combinations of acupoints with highsynergistic efects.
From an empirical perspective, the key acupoints explored from ADN have a strong stability in the diagnostic pattern.Te diversity of acupoints used in acupuncture treatment is a result of the diagnostic patterns of diferent practitioners.Te choice of diagnostic modality depends on the clinical experience and medical knowledge of the physician, and bias in the outcome of modality selection is inevitable.In [46], the authors showed by using network and text mining analysis methods that the best acupoints for a specifc disease can be determined by analyzing diagnostic patterns.Medical data extracted from case reports in [46] to reveal the association between such patterns and acupoints prescribed in clinical practice.In [46], the fve most common diagnostic patterns are listed and the fve highest frequencies of acupoints in the corresponding diagnostic pattern are given and calculated separately.Te most frequent ones, ST36, LI4, KI3, LR3, and SP6, are included in the set of key acupoints identifed by the algorithm.Tus, the key acupoints showed a strong stability in the diagnostic pattern.When selecting certain prescription acupoints based on symptoms, prioritizing key acupoints has implications for improving the accuracy of prescriptions.
Inevitably, this research has some limitations.Te ADN network is still constructed based on pairwise relationships, and the diference from the previous work is that this paper's work introduces 3-node higher-order interactions to reconstruct the weights of the network.From the experimental results, the MPR algorithm outperforms other algorithms in terms of accuracy, resolution and network efciency, and has better adaptability and accuracy.Te key acupoint mining algorithm using higher-order interactions is able to capture more valid information in the network, which helps to explore the potential relationships between acupoints from the perspective of higher-order interactions.However, the information of disease acupoints contained in the network is still limited by the ability to represent pairwise relationships.To address the shortcomings of network representation, in addition to introducing the concept of modalities in the network, higher-order networks can maximize the representation of higher-order interactions among acupoints.Second, due to the limitation of experimental data, the current research on the existence and visibility of the human meridian system has made signifcant progress, but the full distribution information of human meridians is not available, which makes the data sources available with diferent degrees of information loss.In future research, we will use higher-order networks such as hypergraphs or simple complex to break through the limitations of the original networks and further investigate the key acupoint groups and the potential associations between acupoints.Te synergy between acupoints makes the potential association information among acupoints, and the mining and prediction of this potential association information by relying on the higher-order link prediction method can help researchers to reveal the functional and distribution characteristics of human meridians.

Conclusions
As a traditional medical method, acupuncture has an important medical value and reliable clinical efcacy.Currently, scholars have applied network science initially to the study of disease-acupoint relationships.Tis research work constructs an ADN based on clinical acupuncture prescription literature.By introducing higher-order interactions of 3-node motifs on the ADN, the edge weights of the network are reconstructed, and the MPR key acupoint mining algorithm is proposed.Using the MPR algorithm, key acupoints are selected for each region.Compared with other evaluation metrics, the higher accuracy of this metric culture can provide a better combination of acupuncture points as a reference.On this basis, the acupuncture prescription can be optimized and improved, which will reduce the diferences in acupoint selection caused by subjective factors and improve the efciency and efectiveness of acupuncture treatment.In future studies, we will use higherorder networks such as hypergraphs or simple complex to break through the limitations of the original network and further investigate the potential associations between acupoints.Second, for specifc symptoms, we collect fnegrained data corresponding to the symptoms and model them in a more refned manner to fnd key combinations of acupoints for specifc symptoms.

2
Evidence-Based Complementary and Alternative Medicine recorded in 5733 Chinese acupuncture clinical literature.

Figure 1 :
Figure 1: Data acquisition process for the second part of the dataset.

Figure 2 :
Figure 2: Network models of ADN: in the network model, the color and width of edge refect diferent weights and the size of node refects the frequency of utilization.

Figure 6 :
Figure 6: Te example of weight matrix: (a) the traditional adjacency weight matrix; (b) the synergy strength matrix.

Figure 7 :
Figure 7: Te toy examples for the WC model.

Figure 8 :
Figure 8: Te complementary cumulative distribution function (CCDF) for the ranking distributions of ranking list ofered by six algorithms.

Table 1 :
Literature review summary.

Table 3 :
List of softwares.
centrality considers not only the degree of the node itself, but also the degree of the node's neighbors.Te CLD integrates the local clustering characteristics of nodes and their neighbors, and is a new key node mining algorithm.Te key node algorithm considers the product of weights on all paths from node u to other nodes, which measures the importance of the node in the global network.

Table 4 :
Comparison results between MPR and CC. two algorithms in Table 4 provide the top 3 acupuncture points for each of the 19 regions.Te locations highlighted in bold are used to indicate the regions where the two algorithms yield divergent results. Te

Table 5 :
Comparison results of the network efciency.

Table 6 :
Comparison results of the accuracy.