In this paper, we mainly focus on exploring the roles of different government departments and public organizations in promoting the integration of elderly nursing and elderly healthcare. To this end, we constructed the HnICN and explored the connections between different network nodes under a quantitative analysis perspective. In particular, there are three significant strategies in analyzing the HnICN, i.e., the node identification strategy (NIS), the local adjacency subgroup strategy (LASS), and the information collaboration effect measurement strategy (ICEMS), where adopting the NIS can identify the important department nodes and the connections between different nodes, while adopting the LASS can obtain the attribute characteristics of the subgroups. In addition, the ICEMS aims to measure the collaboration effects of different node-pairs, which is the most significant part in the HnICN. The specific details of these three strategies are described as follows.
3.1. The Node Identification Strategy (NIS)
As mentioned above, this paper mainly focuses on optimizing the information collaboration status between different government departments and public organizations for promoting the integration of elderly healthcare and elderly nursing by exploring the HnICN, which means that if we can analyze the information connections existing in the different nodes, identify the important node in the current network, and eventually conclude the corresponding regularity, we will provide valid decision supports to promote healthy aging. To achieve this research purpose, we searched for the powerful evidence in the relevant policy documents issued by China’s government. Therefore, we adopted the named entity recognition method [
20,
21] to identify the network nodes of the HnICN, i.e., the government departments and public organizations mentioned in the relevant documents, and utilized the social network analysis [
22,
23] to explore the relationships between different nodes.
In terms of the node recognition, the method utilized in this section comprehensively integrates multiple recognition dimensions, such as the word frequency, the part of speech, and the length of the word, which divides the names of China’s government departments and public organizations into three parts, i.e., the prefix word (P), the middle word (M), and the tagged word (T), where the tagged word (T) is the core part in the recognition process. In addition, because many pronouns and abbreviations can be used to denote these government departments and public organizations in the common expressions, this paper further optimizes the original dictionary used in the named entity recognition process by collecting and adding theses corresponding pronouns and abbreviations [
24,
25,
26]. The node recognition processes of the NIS are shown in
Figure 2.
In terms of relationship recognition, the existence of information connections between any two identified nodes means that there are some relationships between these two nodes. For example, if two different departments or organizations are mentioned in the same document, it indicates that the promotion of this matter requires the joint participation of these two institutions; in other words, an information collaboration relationship has been generated between these two institutions. Notably, the node importance is a significant attribute, which has a great impact on the node relationships in the HnICN. Therefore, we adopted the degree centrality of the social network analysis to elaborate the importance of different nodes, where the calculation process of degree centrality is as follows:
In Equation (1), the degree_ceni indicates the degree centrality of the nodes, the i and the j are two different nodes, the n is the number of nodes, and the value of connection(i, j) could be taken as 0 or 1, where if there is a connection between the node i and node j, the connection(i, j) is taken as 1, otherwise, the connection(i, j) is taken as 0.
3.2. The Local Adjacency Subgroup Strategy (LASS)
Each node involves a different number of connections in the HnICN, so the network structure of HnICN is a topology with different densities for each node [
27,
28], where the density indicates the potential collaboration range of each node. In fact, the information collaboration process related to a certain matter may require multiple departments’ participation. For example, we assume that the completion of a certain matter needs the participation of department 1, department 2, department 3, and department 4, containing two information transmission processes, i.e., the “department 1→department 2→department 3” and the “department 4→department 3”, which shows that these 4 departments have different collaboration ranges and play different roles in the collaboration processes. In that case, if we can obtain the collaboration range of different nodes, we will discover the pathway for optimizing the structure of the HnICN. Therefore, we designed the LASS to construct subgroups and proposed the concept of collaboration coverage. Notably, the LASS adopts a clustering idea [
29,
30] to transform the relationship between the nodes into that between the subgroups [
29], where each node could be selected as a center of a subgroup and each subgroup can be formed by other non-central nodes which all have connections with the selected center node.
As mentioned above, the subgroup is a significant concept to deeply describe the role that a node plays in the HnICN; moreover, the collaboration coverage results could be obtained based on the subgroups. Specifically, there are two important attribute variables in the subgroup, i.e., the index weight and the node weight. In terms of the index weight, because the analyzed data samples are the government documents, where the target information about the integration of elderly healthcare and elderly nursing is mainly focused on a few fixed aspects, we should transform these aspects into a few analyzable indexes. In fact, the number of departments or organizations involved in each aspect is different, which means the analyzable indexes could have some impacts on the role of different nodes played in the HnICN. Therefore, we need to calculate the index weight in the subgroups. According to the guiding ideology of the SOFPDCHE and the related literature [
31,
32,
33,
34], we eventually concluded five important indexes, i.e., the main policies, the medical resources, the natural resources, the economic support, and the personnel training and employment encouragement. Meanwhile, we adopted the entropy method [
35,
36,
37] to measure the weight values of these five indexes. The specific calculation processes of the index weight are shown as follows:
Equations (2)–(5) mainly focus on the weight computing of the five aforementioned indexes, where the data(i, j) indicates the number of mentions of the ith department in the jth index aspect (in this paper, the data(i, j) is the results after normalization, and the value range is from 1.0 to 2.0), the p(i, j) indicates the proportion of the jth index among all indexes which are related to the ith department, the n is the total number of department nodes, the inf_entropyj and the inf_utilityj are the information entropy of the jth index and the information utility of the jth index, respectively, and the weight_indexj is the final weight result of the jth index.
In terms of the node weight, we introduced the TOPSIS method [
38,
39,
40] and measured the node weight of different nodes based on the index weight calculation results, which are shown as follows:
Equations (6)–(12) aim to describe the computing process of the node weight, where the Z(i, j) is a normalization matrix, and the min(data(j)), the max(data(j)), the (Z(i, j)), and the (Z(i, j)) indicate the minimum value of the jth index, the maximum value of the jth index, the maximum value of each column in the matrix Z(i, j), and the minimum value of each column in the matrix Z(i, j), respectively. In addition, the , the , and the closei represent the distance from the best solution, the distance from the worst solution, and the relative closeness results, where the m indicates the number of indexes.
In addition, inspired by the literature [
41,
42], we adopted an average connection distribution of a certain subgroup to calculate the collaboration coverage of this node, where the collaboration coverage denotes the potential collaboration range of a certain node, which emphasizes the node’s collaboration ability. Therefore, the collaboration coverage can be calculated as in Equation (13):
where the meaning of the
adj_par is an adjust parameter which can be set manually (we set the value of the
adj_par to 10), the
count(subgroup(i)j, centeri) indicates the number of connections between the non-center nodes and center node
i, the
subgroup(i) indicates a subgroup which selects the node
i as the center node, and the
amount(ψ) is a counting function to calculate the number of all nodes in a subgroup.
3.3. The Information Collaboration Effect Measurement Strategy (ICEMS)
The NIS and the LASS can be utilized to analyze the HnICN under a global perspective and a local perspective, respectively. However, we still need to explore the inner relationships of a certain node-pair by analyzing the collaboration degree between these two nodes. Therefore, we proposed the ICEMS to measure the information collaboration effect between different nodes.
Generally, the information collaboration process requires at least two nodes to participate, which means the participation tendency or possibility of each node in the collaboration process is also an important factor to influence the collaboration results. In other words, if a node has a superior potential collaboration range but a low participation tendency, the corresponding collaboration processes which contain this node have difficulty achieving the desired results. In addition, the transmission object in the collaboration process is the information about the integration of elderly healthcare and elderly nursing; therefore, we introduced the information entropy theory [
43,
44] to design the collaboration structure entropy, which is used to describe the collaboration tendency of a node. The calculation process of the collaboration structure entropy is shown as Equation (14):
where the
cse(i) is the collaboration structure entropy of node
i. Based on the collaboration structure entropy, we could obtain the collaboration effect measurement process as follows:
where the calculation process contains two situations for avoiding the maximum value reaching 100% and making the calculation results within the percentage range of 0–100% (in this paper, the parameter
ψ was set to 10,000).