Understanding the Hierarchical Relationships in Female Sex Workers’ Social Networks Based on Knowledge, Attitude, and Practice

Female sex workers (FSWs) represent a high-risk population for HIV infection and transmission. In general, their fellow FSWs (peers) also play a role in their level of susceptibility to HIV/AIDS. This paper draws from interview data of 93 FSWs to construct a multi-layer FSW social network model based on their knowledge, attitude, and practice (KAP). Statistical analyses of the correlation among the three dimensions of KAP as well as their social interactions indicated that FSWs had basic knowledge of HIV/AIDS prevention but demonstrated little enthusiasm in acquiring relevant information. Their knowledge, attitude, and practice were highly positively correlated. Their attitude was more likely to be negatively influenced by their companions, while their practice was more likely to be positively affected. Besides, FSWs exhibited high homophily in KAP with their neighbors. Thus, during HIV/AIDS interventions, FSWs should receive individualized education based on their specific KAP. Considering the high level of homophily among FSWs, their propensity to be positive or negative in their KAP are significantly influenced by their companions. Making full use of peer education and social interaction-based interventions may help prevent and control the spread of HIV/AIDS.


Introduction
In China, heterosexual behavior is one of the main modes of human immunodeficiency virus (HIV) transmission [1]. In fact, the proportion of people who become infected due to the fact of heterosexual behavior has increased over the last decade. In 2007, it was the cause of only 36.1% of cases [2], while in 2017 (as of 31 October), that figure reached 68.50% [3]. This large increase may be somewhat attributed to the behaviors of female sex workers (FSWs)-women who make a living by providing paid sexual services. They are a high-risk population for HIV infection and transmission because they have multiple sexual partners and engage in risky sexual behaviors (such as low rates of condom use during commercial sex) and, therefore, represent a key link in the spread of HIV from high-risk groups to the general population [3,4].
According to the literature, active sexual behavior, limited education, and sensitive interpersonal relationships characterize most FSWs [5,6]. Indeed, a majority lack knowledge about HIV/AIDS

Data
We collected data through one-on-one interviews with FSWs at different locations in a city in Yunnan province, China, between November 2014 and April 2015. First, we randomly chose a number of workplaces to visit and asked the shop owner to agree to interviews. The venues included bars, hair salons, karaoke halls, massage parlors, nightclubs, and hotels. A stratified random sampling method was used to reach these workplaces based on their distribution of workplace counts in that city to avoid a sample bias [41,42]. Then, we interviewed all the FSWs who were there but not in service at that time, one by one. We spent approximately three months collecting the FSWs' responses to the questions (see Table A1) related to HIV/AIDS knowledge, attitude, and practice (KAP). We referred to the AIDS Indicator Survey and previous AIDS KAP questionnaires and adapted them for FSWs in regard to Chinese cultural and ethnic customs. We also interviewed the shop owners (most were also FSWs) whom the other FSWs worked for. Then, it took us an additional three months to acquire the acquaintance relationships among these FSWs (i.e., whether they have social interactions with each other). In total, we gathered 93 responses from 10 workplaces.
As a limitation, we realized that the sample size was relatively small, and it may not be representative. Thus, our research may be illustrative in nature. However, the small sample seems quite common in similar topics due to the difficulty in data collection through surveys and interviews. For example, Battiston (2014) [43] proposed a similar theoretical method, namely, conditional probability combined with a complex network structure to study the existence of correlations across the layers of a multiplex using 78 Indonesian terrorists. Another study (Tuchker et al., 2011) [44] used 62 FSWs to examine how social relationships affect their behavior toward preventing HIV.

Interview Questions
In the AIDS KAP questionnaire, questions on knowledge include understanding of HIV/AIDS, transmission, and risk factors; questions on attitudes include voluntarily taking part in HIV/AIDS prevention training or taking the initiative to understand HIV/AIDS prevention; and finally, questions on practices include safety measures and high-risk sexual behaviors. Table 1 shows a small sample of the responses from the 93 FSWs interviewed (refer to Table A1 for a complete list). Table 1. Knowledge, attitude, and practice toward HIV/AIDS transmission and control (n = 93). Note that Questions 1 to 3 relate to knowledge; 4 and 5 to attitude; and 6 and 7 to practice. Most FSWs knew some information about HIV/AIDS. They had a basic understanding of HIV transmission routes, prevention practices, and the associated risk. However, over half still had some misconceptions. For example, 63 respondents mistakenly believed mosquito bites can transmit HIV. Although a few had proactively sought out information on HIV/AIDS (e.g., through radio, television, traditional media, etc.), most were quite passive in HIV/AIDS prevention. Most had only sought out a few voluntary HIV tests and did not participate in public service activities, such as free HIV/AIDS counseling, free condoms or prevention skills training (only 1 of the 93 FSWs).

The Division of Node Attribute
The primary goal of the HIV/AIDS intervention program is to convert "negative" FSWs into "positive" ones, or in other words, help FSWs have more knowledge, have fewer misconceptions, and engage in safer sexual practices in terms of HIV/AIDS transmission. The more questions answered correctly, the more positive she is, and the more questions answered incorrectly, the more negative she is. According to our previous study [45], we used Z-scores to identify the relative positivity or negativity of FSWs based on their respective responses to KAP questions. This standardization method measures the distance between an individual and the mean; thus, a relatively large Z-score often indicates an individual has answered more questions correctly, i.e., the individual is more positive. Please note that we use the terms "negative" and "positive" in a relative sense as worse or better, but not in an absolute term.
Counting FSWs' responses to all the interview questions in one category (or attribute layer α, here α = K, A, P; where K, A and P denote knowledge, attitude and practice respectively), let T . the standard deviation. We used the following Equation (1) to calculate the Z-scores of all FSWs in layer α: when Z [α] i ≥ 0, we consider the FSW to be positive; otherwise, she is considered negative. It is worth pointing out that, although we subjectively distinguished FSWs into positive ones and negative ones according to their average performance, we actually mean that positive FSWs are more active than negative ones, which is not an absolute judgment.

FSW Social Network
We built the social interaction network of FSWs based on acquaintance relationships. The network designates FSWs as nodes and the social relations among FSWs (acquaintance or not) as edges (relationship). The FSW social network can be represented by a graph G(N, A), which consists of nodes set N and edges set A. Among them, each FSW is uniquely represented by a node ID number, and the edge set could be translated into an adjacent matrix K = k ij , in which k ij represents the social relationship between node i and node j. If i and j are acquaintances, then they are directly connected and k ij = 1 ; otherwise k ij = 0 . We visualized the network in Figure 1 below.
As shown in Figure 1, we divided the FSW nodes into five sections, each one a different color to represent a different type of workplace. Nodes 1 to 25 work in a bar or karaoke hall, 26 to 48 a salon, 49 and 50 a sauna or massage parlor, 51 to 57 nightclubs or hotels, and 58 to 93 other workplaces. The node size reflects the amount of social connections the FSW has in the network; thus, larger ones represent FSWs who know a larger number of their peers in this study. On another level, the size could also be a reflection of one's social skills and importance to the entire network. network designates FSWs as nodes and the social relations among FSWs (acquaintance or not) as edges (relationship). The FSW social network can be represented by a graph G (N, A), which consists of nodes set N and edges set A. Among them, each FSW is uniquely represented by a node ID number, and the edge set could be translated into an adjacent matrix = { } , in which represents the social relationship between node i and node j. If i and j are acquaintances, then they are directly connected and = 1 ; otherwise = 0 . We visualized the network in Figure 1 below. As shown in Figure 1, we divided the FSW nodes into five sections, each one a different color to represent a different type of workplace. Nodes 1 to 25 work in a bar or karaoke hall, 26 to 48 a salon, 49 and 50 a sauna or massage parlor, 51 to 57 nightclubs or hotels, and 58 to 93 other workplaces. The node size reflects the amount of social connections the FSW has in the network; thus, larger ones represent FSWs who know a larger number of their peers in this study. On another level, the size could also be a reflection of one's social skills and importance to the entire network.

Multi-Layer FSW Social Network
Next, we built a weighted multi-layer FSW social network based on (1) the social relations among FSWs and (2) their positive and negative Z-scores at different layers. We calculated the weight of a node in the multi-layer network as follows: First, when node was part of a positive group in the layer (i.e.,   0

Multi-Layer FSW Social Network
Next, we built a weighted multi-layer FSW social network based on (1) the social relations among FSWs and (2) their positive and negative Z-scores at different layers. We calculated the weight of a node in the multi-layer network as follows: First, when node i was part of a positive group in the α layer (i.e., Z i . Accordingly, W i = 3 − W i represents the negative weight of node i. Based on the positive and negative weight of node i, Figure 2 illustrates the multi-layer FSW social network.   Figure 2a, the red-colored nodes are positive in all three layers, while in Figure  2b, the light blue ones are negative in the practice layer and positive in the knowledge and attitude layers. As for size, in Figure 2, it reflects the scale of the node's absolute value. That is, a larger node indicates this FSW is more positive (in Figure 2a) or negative (in Figure 2b).   Figure 2b, the light blue ones are negative in the practice layer and positive in the knowledge and attitude layers. As for size, in Figure 2, it reflects the scale of the node's absolute value. That is, a larger node indicates this FSW is more positive (in Figure 2a) or negative (in Figure 2b).
As we can see from Table 2 and Figure 2, of the 93 FSWs, 16 and 19 have three positive or negative Z-scores, respectively, while 58 have both positive and negative Z-scores in different layers. In addition, 22 FSWs have positive Z-scores in a single layer and negative in the other two layers. In total, most FSWs are positive in at least one layer. However, the shop owners, in particular, have special features in the multi-layer FSW social network. In fact, 33.3%, 11.1%, and 55.6% are negative in three layers, two layers, and a single layer, respectively. In other words, none of the shop keepers are positive in all the three layers, while 19.5% of the other FSWs are, in contrast. Compared to the latter, they tend to be even more negative in terms of HIV/AIDS prevention. Considering their wider range of social connections and greater degree of influence, they may have a more significant negative impact on their acquaintances than the non-shop keeper FSWs do. Thus, it is especially important to reach out and educate shop owners.

Positive and Negative FSW Social Sub-Networks
To further analyze the interaction of the FSWs, we extracted the weighted positive and negative sub-network in the knowledge, attitude, and practice layers, respectively, from the multi-layer FSW social network. Let T i increases, the FSW is more negative. Figure 3 lists the extracted positive and negative sub-networks. Figure 3a-c represent the positive sub-networks of the knowledge, attitude, and practice layers, respectively, while Figure 3d-f represent the corresponding negative sub-networks. Different workplaces and the positive (negative) level of nodes are respectively distinguished by color and size. The nodes in the red circles are shop keepers.
Compared with the FSWs working in a salon, bar or karaoke hall, those working in high-end venues, such as nightclubs and hotels, tend to be more positive, as shown in Figure 3 and Table 3.   Compared with the FSWs working in a salon, bar or karaoke hall, those working in high-end venues, such as nightclubs and hotels, tend to be more positive, as shown in Figure 3 and Table 3.

Measuring the Association between Responses to Knowledge, Attitude, and Practice
First, we used a probabilistic method (i.e., conditional probability) to measure the association of an individual's responses to KAP. Let a On the condition that node i is part of a positive group in α layer, the probability that node i is also part of a positive group in α layer is as shown in Equation (4): Let O [α] denote the set of positive FSWs in the α layer, and O g becomes more positive. Then, we used Equation (5) to calculate the probabilities of positive node i in subset O [α] g also being positive in layer α , as shown in Figure 4a-c. Figure 4a-c represent the correlations of positive individuals' performance in KAP when α is knowledge, attitude and practice, respectively. Similarly, we also used the same equation to calculate the probabilities, of negative node i also being negative in layer α as shown in Figure 4d-f. Figure 4d-f represent the correlations of negative individuals' responses to KAP when α is knowledge, attitude, and practice, respectively.
. On the condition that node is part of a positive group in layer, the probability that node is also part of a positive group in ′ layer is as shown in Equation (4): Let becomes more positive. Then, we used Equation (5) Table A2 for the fitted equations and parameters of the models as well as the results of significant testing. We only provided the conclusions when the fitted lines passed the related significant testing.
In general, the results indicated a strong positive correlation among responses in the knowledge, attitude, and practice layers. For a node, the more positive an FSW was in layer, the higher the probability she was positive in the other two layers. For example, the more positive a node was in the attitude layer, the higher probability of being positive in the knowledge and practice layers (as shown in Figure 4b). With the increase of the probability of nodes being positive in the knowledge layer, the probability of being positive decreased before rising in the other two layers (Figure 4a). In particular, there were several fluctuations when g = 11 and g = 13 in the knowledge layer. The key reason was that the subsets of 11 [ ] and 13 [ ] mainly included FSWs who worked in a bar, karaoke hall, and other venues. The FSWs in those workplaces were characterized by positive knowledge, but negative attitude and practices. Meanwhile, when g = 5, the inclusion of shop owners (half of the  Table A2 for the fitted equations and parameters of the models as well as the results of significant testing. We only provided the conclusions when the fitted lines passed the related significant testing. In general, the results indicated a strong positive correlation among responses in the knowledge, attitude, and practice layers. For a node, the more positive an FSW was in α layer, the higher the probability she was positive in the other two layers. For example, the more positive a node was in the attitude layer, the higher probability of being positive in the knowledge and practice layers (as shown in Figure 4b). With the increase of the probability of nodes being positive in the knowledge layer, the probability of being positive decreased before rising in the other two layers (Figure 4a). In particular, there were several fluctuations when g = 11 and g = 13 in the knowledge layer. The key reason was that the subsets of O 13 mainly included FSWs who worked in a bar, karaoke hall, and other venues. The FSWs in those workplaces were characterized by positive knowledge, but negative attitude and practices. Meanwhile, when g = 5, the inclusion of shop owners (half of the FSWs in this group) resulted in a decreasing tendency of being negative in the knowledge layer (as shown in Figure 4f); they generally exhibited positive knowledge but negative practice.
In addition, an increase in a node's negativity in the attitude layer led to an increase in negativity in the practice layer. However, it is difficult to determine whether the node tended to be negative or not in the attitude layer alongside an increase in negativity in the practice layer. This indicates that attitude can affect practice, but the reverse may not be true. Moreover, other factors besides attitude, such as workplace requirements, may influence behavior.

Measuring Neighbor Impact on an Individual in a Single Layer
A FSW's companions-her neighbor nodes in the social network-may influence whether she is positive in a layer. To determine this, we measured neighbors' impact on an individual in a certain layer. We started from the basic assumption that communication among people can affect each individual's knowledge, attitude, and practices. Then, neighbors' impact on an individual in a certain layer was positively correlated to, on the one hand, the number of her neighbors (i.e., node degree) and, on the other hand, the positive or negative responses of her neighbors (i.e., the neighbors' positive or negative weights) [28]. For example, an FSW would be positively influenced when she has a lot number of friends who have lots of HIV/AIDS knowledge and are very positive on attitude and behavior. Therefore, we looked into a FSW's social environment in a layer based on her neighbors' responses in the same layer, using the sum of weights of all her neighbors as defined below.
For node i in α layer, let p j denotes the weight of positive node j in the positive sub-network of the α layer. A relatively large weight indicates that node j is more positive and has a more significant impact.
Similarly, for node i in the α layer, let n [α] i denote the impact index from negative neighbors in the same layer, as shown in Equation (7). For the neighbors j of node i, R [α] j denotes the weight of negative node j in the negative sub-network of α layer. A relatively large weight indicates the node j is more negative and has a more significant impact.
Let s [α] i denote the impact index of node i from all of her positive and negative neighbors, as shown in Equation (8).   shown in Equation (8).  As shown in Figures 5 and 6, neighbors are more likely to negatively influence attitude than practice, while knowledge and practice are more likely to be positively influenced than attitude.
Especially in the attitude layer, FSWs are not as positively affected by their neighbors (i.e., s

Measuring Neighbors' Influence on an Individual in the Multi-Layer Network
Neighbors influenced FSWs in other layers as well as in the same layer. Therefore, we used a probabilistic method to measure the overall effect of neighbors on an individual in a certain layer, namely, how a FSW's responses were correlated with that of her neighbors-for instance, for a positive FSW in the knowledge layer, how her attitude and practice were correlated with her neighbors' responses.

Positive and Negative Neighbors
This is how we defined positive and negative nodes on the multi-layer network. First, let  i (α = K, A, P) represents the positive level of node i in α layer, while n [α] denotes the total number of questions about α in the questionnaire. Then, by calculating the Z-score of T i , we identified the FSWs as positive or negative nodes. When Z i ≥ 0, we consider an FSW to be positive and otherwise negative.
practice layer are not as negatively affected by their neighbors (i.e., [ ] > 0). In sum, FSWs are more likely to be positively influenced in the knowledge and practice layers and negatively influenced in the attitude layer.

Measuring Neighbors' Influence on an Individual in the Multi-Layer Network
Neighbors influenced FSWs in other layers as well as in the same layer. Therefore, we used a probabilistic method to measure the overall effect of neighbors on an individual in a certain layer, namely, how a FSW's responses were correlated with that of her neighbors-for instance, for a positive FSW in the knowledge layer, how her attitude and practice were correlated with her neighbors' responses.

Positive and Negative Neighbors
This is how we defined positive and negative nodes on the multi-layer network. First, let

Neighbors' Influence on Positive FSWs
For a positive FSW in the layer, we studied her responses in the other layers to consider her neighbors' influence. In other words, for a positive FSW in a certain layer, we determined how her responses (i.e., positive/negative probability in a layer) were correlated with her neighbors' overall

Neighbors' Influence on Positive FSWs
For a positive FSW in the α layer, we studied her responses in the other layers to consider her neighbors' influence. In other words, for a positive FSW in a certain layer, we determined how her responses (i.e., positive/negative probability in a layer) were correlated with her neighbors' overall responses. In the α layer, let q Similarly, the positive ratio in the α layers for the nodes in O respectively. Please refer to Table A3 for the fitted equations and parameters of the models as well as the results of significant testing. We only provided the conclusions when the fitted lines passed the related significant testing.
As shown in Figure 7, for the positive nodes in the α layer, as the proportion of negative (a-c) or positive (d-f) neighbors increased, the probability of being negative or positive at another layer shows a rising trend. The results indicate a strong positive correlation. The higher the proportion of negative (positive) neighbors, the greater the potential negative (positive) influence on the node. Taking Figure 7b,e for example, for the positive nodes in the attitude layer, as their negative (positive) neighbors increase, the probably of being negative (positive) in other layers increases.
For positive nodes in a certain layer, as negative or positive neighbors increase, the probabilities of being negative or positive, respectively, in the other two layers generally rise, albeit at differing slopes. The difference indicates that neighbors have differing levels of impact on individuals in the other layer. For instance, in Figure 7a, Curve P2 sits above Curve P1, which indicates that, for an individual whose neighbor ratio is constant, the probability of being negative in the practice layer is higher than in the attitude layer. Meanwhile, the slope of Curve P2 (0.783) was greater than that of Curve P1 (0.758) (as shown in Table A3). This implies that, when the number of negative neighbors increase, negative neighbors affect the practice of positive nodes in the knowledge layer more so than their attitude. In sum, the probabilities of being positive or negative at the other layers stems from a node's own state (intercept) and neighbors' influence (slope).
If we cross compare the contrasting graphs for the same positive nodes in a certain layer, the differing slopes of corresponding curves, such as Curve P2 and P2 in Figure 7a,b, suggest that negative and positive neighbors of positive nodes in the knowledge layer have differing levels of impact on behavior. Because the slopes of Curve P1 and P2 were greater (as shown in Table A3), this means positive neighbors have a stronger influence than negative neighbors do on positive nodes in the knowledge layer. That is, when the numbers of negative or positive neighbors increase, the positive nodes in the knowledge are more likely to be positively affected.

Neighbors' Influence on Negative FSWs
To investigate the negative influence of neighbors on negative nodes, we studied FSWs' performances in other layers. In other words, for a negative FSW in a certain layer, we looked at how her responses (i.e., positive/negative probability in a layer) were correlated with her neighbors' responses. Let q [α] i denote the positive neighbor ratio of node i, as shown in Equation (11).
The negative neighbor ratio of negative node i is 1 − q Similarly, the negative ratio in the α layers for the nodes in O  i and 1 − q The x-axis represents q    Table A4 for the fitted equations and parameters of the models as well as the results of significant testing. We only provided the conclusions when the fitted lines passed the related significant testing.
As we can see from Figure 8, for negative nodes in layer , as the proportion of positive (negative) neighbor increased, the probability of being positive (negative) in another layer generally shows a rising tendency, which indicates a positive correlation to some degree.
For negative nodes in the attitude or knowledge layers, positive or negative neighbors generally had a more significant influence on their practice as opposed to knowledge and attitude, wherein the negative effects were greater (refer to Appendix Table A3 for the slope values), as shown in Figure  8a,b,d,e. Indeed, the linear regression for practice rose sharply, while the others were more stable. For instance, as shown in Figure 8b, as the number of positive neighbors increased, the practice of the negative nodes tended to be more positive, while their attitude remained essentially unchanged. In addition, comparing Figure 8a,d,b,e, the slopes of P2′ and P4′ were greater than those of Curve P2 and P4, respectively. This indicates that the practice of negative nodes in the attitude and knowledge layers was more likely to be affected by negative neighbors.  Table A4 for the fitted equations and parameters of the models as well as the results of significant testing. We only provided the conclusions when the fitted lines passed the related significant testing.
As we can see from Figure 8, for negative nodes in layer α, as the proportion of positive (negative) neighbor increased, the probability of being positive (negative) in another layer generally shows a rising tendency, which indicates a positive correlation to some degree.
For negative nodes in the attitude or knowledge layers, positive or negative neighbors generally had a more significant influence on their practice as opposed to knowledge and attitude, wherein the negative effects were greater (refer to Table A3 for the slope values), as shown in Figure 8a,b,d,e. Indeed, the linear regression for practice rose sharply, while the others were more stable. For instance, as shown in Figure 8b, as the number of positive neighbors increased, the practice of the negative nodes tended to be more positive, while their attitude remained essentially unchanged. In addition, comparing Figure 8a,d,b,e, the slopes of P2 and P4 were greater than those of Curve P2 and P4, respectively. This indicates that the practice of negative nodes in the attitude and knowledge layers was more likely to be affected by negative neighbors.
For negative nodes in the practice layer, when the number of positive neighbors increased, they were less likely to become positive in the attitude and knowledge layers; on the other hand, when the number of negative neighbors increased, they were more likely to be negative in the attitude and knowledge layers. Overall, negative nodes are more likely to be affected by negative neighbors, and the negative influences are greater than the positive ones.

Discussion
Prior studies and programs among FSWs have reported improvement of HIV knowledge [16,17] and sexual behavioral changes [18,19] by distributing educational materials, providing free condoms, etc. [16]. Those studies largely focused on examining individual attribute characteristics [34,35]. But the mutual influence between peers and acquaintances within a social network has rarely been explored. Based on a multilayer social network architecture, we proposed a probability model to reveal the inter-correlation of FSWs' responses in KAP as well as the relationships between the individuals and their acquaintances or companions. The constructed model combined the individual's characteristics and her structural features in the social network to quantify the impacts the peers have on a focal individual using a statistical probability method.
We found that most FSWs have a passive attitude toward HIV/AIDS prevention although they have a certain understanding of HIV/AIDS. In general, there are strong positive correlations at all layers. For positive FSWs, their attitude is the most likely to be negatively affected, followed by knowledge and practice, while for negative FSWs, practice is the most likely to be positively affected, followed by knowledge and attitude. Based on these findings, HIV/AIDS interventions should be tailored to suit FSWs with different KAP scores. For positive FSWs, it is necessary to pay more attention to attitude to help prevent negative influences. For negative FSWs, more attention should be paid to their neighbors and peer education because they are more likely to be influenced by negative neighbors.
In general, negative FSWs exhibit high homophily in knowledge, attitude, and practice with negative neighbors, while positive FSWs exhibit homophily in knowledge with positive neighbors. For positive FSWs in the knowledge layers, positive neighbors are more likely to affect them so they might become positive in all three layers more easily than other nodes. Therefore, programs should make full use of peer education, namely, working with positive FSWs to strengthen HIV/AIDS prevention. As for FSWs with negative Z-scores, they are more likely to be affected by positive neighbors in practice than in knowledge and attitude. So, relevant policies concerning practice to improve the effectiveness of intervention and education programs should be made.
Since the KAP framework describes a kind of sequential or causal relationship, measuring the conditional probability that a FSW positive in knowledge is also positive in attitude or practice provides enough implications. However, a reverse path from practice to knowledge/attitude also gives contributions. In fact, the sequential relationship described by the KAP framework is not an inevitable causal relationship, but a probability relationship. For the FSWs, there are many impact factors that would make their behaviors changed, such as social culture, customs, habits, public opinion, laws and regulations, etc. Therefore, behavioral changes of an FSW does not depend solely on the shift in knowledge or in attitude. In other words, for the positive FSWs in practice, their knowledge and attitude are not necessarily positive. In the future, we will try to quantify the impacts on their behavior caused by knowledge change, as well as other impact factors, to find efficient approaches to make FSWs more positive on behavior.
There is also much future work that may further extend this study. For example, this study collected individual characteristic and network structural information through interviews with 93 FSWs. We assumed the responses were truthful. However, the use of a questionnaire might be subject to social desirability or other systematic biases [44,[46][47][48][49][50]. In the future, we could explore more representative and comprehensive datasets with alternative data collection approaches. For example, we can rely on log data or social media data from online communities and platforms of FSWs [51,52]. We could also devote ourselves to interviewing more FSWs at different workplaces and/or in different districts or areas to provide more generalizable conclusions.

Conclusions
Female sex workers have drawn a lot of attention in the context of HIV/AIDS prevention. In this paper, we used a knowledge, attitude, and practice (KAP) questionnaire to explore the correlations among these three aspects based on the social networks of FSWs. We interviewed FSWs on their KAP  Table A2. Fitted equations and parameters for the curves in Figure 4.   Table A4. Fitted equations and parameters for the curves in Figure 8. The number of positive responds showed by node i at α layer

Sub-Graph
The mean of the number of positive responds showed by node i at α layer σ [α] The variance of the number of positive responds showed by node i at α layer The Z-Score value of node i at α layer W i The positive weight of node i in the multi-layer FSW social network W i The negative weight of node i in the multi-layer FSW social network The number of negative responds showed by node i at α layer The weight of positive node i at α layer The weight of negative node i at α layer   Using the contingency table above, we calculated the chi-square values and their statistical significance (p-values) for the FSWs in the knowledge layer, as shown in Table A7. Then we obtained the chi-square test results for the FSWs in the attitude and practice layers.