TRTCD: trust route prediction based on trusted community detection

Social networks have become increasingly popular and are used for various activities. It is essential to evaluate the trustworthiness of the path between two unknown users in social networks. However, there are usually many social routes between them. In applications of trust, confidence relations among users need to be predicted. Trust route prediction predicts a new trust relationship between two users who are not currently connected. Thus, a challenging problem is finding which social trust route is optimal to yield the most trustworthy route. As a result, this process faces many challenges, such as the sparsity of user-specified trust relations, context awareness of trust, and changes in trust values over time. A new trust route prediction framework was proposed in this paper to enhance prediction accuracy. Considering community relations and node information for community detection, the proposed trust route prediction algorithm, TRTCD, is introduced. The effect of node and community information on link prediction accuracy was empirically investigated here using seven parameters. Experiments on eleven real-world datasets showed that the proposed method performed better than the fourteen existing methods. Based on the obtained experimental results, the proposed method performs better than other methods regarding accuracy and cost. The results show that the TRTCD has, on average, 22% better on eight directed datasets. The results of the NDCG measure show that the TRTCD can reach the average value of trust very close to 1, which is outstanding and performs better than other algorithms in terms of the ATCE criterion since more trusted and integrated communities are identified. In addition, the results show that the TRTCD can be successfully used in directed social networks but needs to work better in undirected social networks.


Introduction
A network can be defined as a structure composed of nodes and the static or dynamic relations between them, which are referred to as edges or links.A wide variety of complex systems can be modeled by the simple structure, including social, biological, and technological systems, where the system entities are represented by nodes, and their interrelations are indicated by edges [3,13].Network mining studies and complex network analyses have been inspired by data proliferation.There have been a large number of investigations of problems concerning network mining, including community detection [18,84], node ranking [59,85], and network embedding [41].Among them, link prediction has increasingly appealed to various fields because many of the available real-world datasets are incomplete [88,89].It has also a wide variety of applications in reality as well as in theory [64,69].Link prediction can be utilized, for instance, in the exploration of network evolution mechanisms [106,107], obtaining the opportunities for cooperation among scientists [102,104], recommending friends in a social network [28,67], and discovering the protein-protein interactions in a biological network [15,43].The link prediction task involves an inference of the missing or future interactions of nodes forming pairs according to their features and the network structures that are observed currently [64,69,95].In fact, it is difficult in most cases to obtain information on node features in a real-world network due to privacy or data collection reliability issues, which explains the plenty of attention attracted by link prediction methods that are based on network structure information.
These methods can be categorized broadly into similarity-based and learning-based ones [58,69,95].Estimating the similarity scores of target node pairs, a similarity-based method supposes that missing links are more likely to occur for pairs of nodes with higher scores.In the learning model, a training set is generated from observed links of a network.The learningbased method uses the learned model to predict the probability of potential links in the network.These methods are subcategorized into classification-based, probabilistic and statistical, and matrix factorization methods.A classification-based method formalizes link prediction as a problem of binary classification [21,76].Each of the samples in the training set involves a pair of nodes with a series of features and a class label.The features of the pair, including reciprocity, transitivity, and common neighbors [27], are extracted from the observed network structures.A pair of nodes is labeled as positive if there is a link between the relevant nodes and as negative, otherwise.Supervised learning approaches, including support vector machines, decision trees, k-nearest neighbors, and neural networks [113], are then used for learning prediction models.A network formation process is assumed by a typical probabilistic or statistical method to be compliant with a known structure.These methods generate models, such as hierarchical structure [20], stochastic block [43], and forward generative [54] models, to fit the structure and estimate the linkage probability of non-observed links.A matrix factorization method considers link prediction as a matrix completion problem, capable of making predictions by extracting latent features and/or using additional ones [33,70,75].Pech et al., for instance, introduced robust principal component analysis to decompose the adjacency matrix into two components: a low-rank matrix that represented the network backbone and a sparse one that indicated the spurious links in the network [75].
The purpose of this paper is to detect and introduce a trust route through the identification of trust communities for detection of more accurate trust links using the clustering method and considering a number of new parameters including the effect of community trust link power.We first detect trust communities and then find a trust route between the nodes of source and destination on the most trusted communities.In fact, the best trust route is introduced between the two input nodes (source and destination), which includes a list of nodes with the highest value of trust.
The reminder of this paper is organized as follows: related work is presented in Section 2. Section 3 describes research methodology, and parameters.The experimental results are presented in Section 4, including the datasets, evaluation metrics, and compared methods.The paper finishes with Section 5, where the main conclusions are presented.

Related works
So far, many suggestions have been made for link prediction methods to be used in various areas.Such as direction of the laboratory experimentation in a dataset involving the interaction among proteins [23], recommendation of friendships in online social networks (such as Twitter and Facebook) [26,50,93], recommendation of products to target users on an e-commerce website [66], and even for detection of spurious links in different networks in a noisy environment [73].
Ma et al., on the other hand, developed methods of link prediction in a dynamic network using the data time series [68,110].A new graph convolutional neural network was proposed by Zitnik et al. for the prediction of multi-relational links in a multimodal network [113].There are two broad classes of existing link prediction algorithms and models, involving the community information-based models and similarity-based algorithms.Besides the observed network structure, the probabilistic models usually require information on vertex attributes.Hence their higher time complexity, makes them often hard to apply to large-scale datasets [106].
A typical similarity-based algorithm assigns a score to each vertex pair to quantify the probability of link existence.These algorithms are used widely due to their prediction accuracy and calculation efficiency [100].They can be subdivided into two categories, based either on local information (local indices) or on global information (global indices).Local indices are more efficient than global indices due to their lower computational complexity, while they are less accurate, on the other hand [64].
Given that a typical real-world network is large-scale or even super-large-scale, plenty of research is focused on local indices, which are less time-consuming and easy to implement in a large-scale network.Except a few classical local indices based on common neighbor nodes, including Adamic Adar (AA) and Resource Allocation (RA), they assume that all common neighbors have the same effect on the probability of a link, which restricts their accuracy.Feng et al. [25] concluded through experimentation over real-world and synthetic datasets that network community structure growth could considerably enhance the accuracy of similaritybased methods.The above finding has motivated a large number of researchers to propose a variety of link prediction methods according to clustering or community information (CI) to enhance the accuracy of prediction [22,56].For the same purpose, Soundarajan and Hopcroft integrated the RA and Common Neighbors (CN) indices [87].Valverde-Rebaza and Lopes [94] proposed a method referred to as WIC, which used information from intra-cluster (withincluster, W) and inter-cluster (IC) common neighbors, demonstrating that CI always makes sense regardless of the choice of clustering algorithms.They applied WIC to Twitter, which is recognized as a directed asymmetric large-scale online social network [93].
Li et al. [55] used parameter adjustment to develop a method based on CI and the Preferential Attachment (PA) index.Wang et al. [97] proposed ICRA, a method based on intra-community (Intra-Com) information and the RA index, exhibiting the highest overall performance over ten real-world datasets.To use the prior CI on link evolvement, Jeon and Kim [48] proposed a community-adaptable method of link prediction.Most of these methods, however, simply considered the impact of Intra-Com common neighbors, disregarding the others.

Link prediction algorithms
& Link prediction based on similarity Preferential Attachment index [6], defines the score of similarity of two target nodes as the product of their degrees.The simplest similarity-based method, the common-neighbors (CN) index is calculated as the number of neighbors that two target nodes share [72].There are a number of indices used for normalization of the results obtained by CN from different perspectives.These include the Jaccard coefficient [60], Hup Promoted index [79], Hup Depressed index [111], and local Leicht-Holme-Newman index [53].The impacts of common neighbors with large degrees are penalized by the AA [2] and RA [111] indices for discrimination of the contributions made by different common neighbors.The probability of connection of a target node pair is estimated in the local Naïve Bayes model [61] based on the Bayesian theory and in the Mutual Information index [90] based on information theory.In both methods, common neighbors are regarded as the feature variables, and are assumed to be independent of one another.Similarly, a model known as Intermediary Probability was proposed for link prediction from the perspective of an intermediary network feature process [109].Cannistraci et al. emphasized the significance of local community links to propose a series of CAR-based indices for the improvement of classical similarity measures [15].The clustering coefficient of a common neighbor is taken in the CCLP index as a contribution to link formation between target nodes [98].The TRA index was proposed recently by Bai et al., emphasizing the significance of the common neighbors that can form triangles with a single target node [5].A number of global and quasi-local methods have been designed in addition to the above local ones.All paths that connect two target nodes are summed in the Katz index, where a smaller weight is assigned to a longer path [51].The global Leicht-Holme-Newman index attributes a similarity proportional to the number of paths between target nodes on the same basis as in Katz [53].
The similarity score of a target pair of nodes is updated iteratively in the SimRank index [47] based on that of their neighbors.Using the paths of lengths 2 and 3 between two nodes to estimate their similarity, the Local Path index seeks to provide a balance between the CN and Katz indices [65,111].The Local Path and Mutual Information indices are integrated in the Neighbor Set Information index, evaluating the contributions made by paths of lengths 2 and 3 in accordance with information theory [112].
The ERA index is an extension of RA, where the resource transfer process of local paths is considered [63].Recently Link prediction approaches based on similarity, structural similarity in particular, are used widely.The local, quasi-local, and global network structures are extracted from the structural similarities for the computation of target link probability scores.CN [72], AA [2], and RA [111] are the most popular methods based on structural similarity.Graph embedding techniques [8,42,77,80], such as logically linear embedding (LLE) [80] and Laplacian eigenmaps [8], both involving simple embedding, have been applied successfully to the problem of link prediction.Their drawback is that they are extremely complicated and hardly scalable in implementation, but they have leveraged network sparsity to enhance scalability.DeepWalk, a local embedding method using local information from random walks, was presented by Perozzi et al. [77].
It maximizes the co-occurrence likelihood of random walks to preserve proximity of higher order.Another model of random walks, known as node2vec, was used in [42] to embed the nodes in the representational space.A tradeoff was established between depthfirst and breadth-first search for performance enhancement.Naderan et al. [71] classify trust in social networks using combined machine learning algorithms and fuzzy logic.First, the raw data of the real-world dataset, Epinions, is examined, and the feature vector is calculated for each pair of social network users.Next, fuzzy logic is incorporated to rank the membership of trust to a specific class, according to two-, three-and five-classes classification.Finally, to classify the trust values of users, three machine learning techniques, namely Support Vector Machine (SVM), Decision Tree (DT), and k-Nearest Neighbors (kNN), are used.
In [83], four new models for estimating the trust mechanism of the users were proposed and analyzed using Kolmogorov-Smirnov and Anderson-Darling statistical hypothesis tests to identify and validate the best-fitted model based on 20,613 empirical results gathered from 4552 social network volunteers.Due to the time-complexity of the problem, a meta-heuristic algorithm based on the Artificial Bee Colony (ABC) optimization method was also developed for solving the best-fitted model.

& Link prediction based on community information
A large number of link prediction models have been proposed to integrate the community information for improvement of prediction accuracy.A framework was proposed in Yan and Gregory [99] according to the idea that unconnected nodes are more likely to involve missing links when they belong to the same community than when they are in different communities.Potential links within a community are ranked there separately from ones between different communities, with the two sequences merged later with the intra-community links followed by the inter-community ones.The WIC index uses information from intra-cluster and inter-cluster shared neighbors to compute the probability of connection of a node pair [94].
An intra-cluster neighbor contributes positively, while an inter-cluster neighbor contributes negatively.The probability of connection is zero, however, for target nodes in different communities or with no intra-cluster neighbors.Edge centrality is used along with community information in the community-based link prediction algorithm [10], which computes edge centrality (EC) and community-based edge weight (CEW) for each of the existing links, the product of which obtains the overall importance of a common neighbor to the corresponding target node.In the computation of CEW, links with end within the same community are assigned positive weights, while the others are assigned negative weights.The modularity contribution measure was presented in the modularity-based link prediction algorithm for prediction of a link between a pair of nodes using their intracommunity and inter-community information [14].Proposing a community bridge boosting prediction model [32], Gao et al. highlighted the role played by bridges, i.e. nodes connected to many communities, in formation of new links, forming the only connections between communities.Unlike other methods, this one enhanced the similarity scores of bridge nodes.Proposing topology-based link prediction, Huang Zan [45] introduced a model of cycle formation using the generalized clustering coefficient for prediction of probability.Ding et al. [24] presented an approach to link prediction where the community structure was extracted under a specific resolution.They then distinguished different communities, and computed the probability scores of target links using a frequency statistical model.The same researchers proposed another similarity feature, referred to as community relevance, considering latent inter-community information besides other information already in use in other link prediction approaches.
A number of recent studies have also integrated link prediction with the information dissemination model [7,16,57,103].A two-step process was proposed by Chaoji et al. [16] for achievement of information relevance as well as efficient content spread.With similar inspirations, Yu et al. [103] used algebraic connectivity regularization to propose a one-step process for the same purpose.Assuming a major role in the generation of links and evolution of networks for diffusion of information, Li et al. [57] presented a link prediction approach over the SINA Weibo dataset.Belkhadir et al. [7] introduced a method called RSTN, in order to achieve better results, the suitable group of friends is clustered and the shortest path between users to have the most trusted users is calculated.

Trust prediction algorithms
In this section, we also describe related works, we broadly divide trust prediction approaches into three categories: interaction-based trust models, graph-based trust models, and hybrid trust models.

& Trust Prediction based on Interaction
These models mainly focus on the interactions among users.Adali et al. [1] developed a trust prediction approach centering on users' communication behavior, trust, and propagation.Forouzandeh et al. [30] reviewed the role of influential nodes on other users on Facebook social media sites by social and behavioral characteristics of users.The authors define a new centrality for users, considering node status and behaviors.Thus, this node has a high level of influence.Sacco and Breslin [82] introduced a trust prediction approach focusing on the subjective trust values of connected users, based on their social interactions; They claimed that most of the existing trust prediction algorithms are 'propagating known trust values among peers in a trusted network and do not provide measures for asserting a trust value from user interactions between peers [82].Yang et al. [101] constructed the relationship between trust and closeness using an ordinary least squares regression model, and the factors that influence trust between social network users with the help of an endogenous switching regression (ESR) model.They constructed a model to assess the characteristic of similarity trust, interaction trust, and platform evaluation trust of social media users.They investigated factors that influence trust between adjacent users in social networks.These approaches only focus on users' interactions and do not consider the social network structure, which may contain important information about users and the type of relations among them.

& Trust Prediction based on Graph
It is assumed that each user has a trust network that includes friends as nodes, and the relationships among them as the edges [86]; although, in some cases, it may fail to capture the actual interactions among members [86].Trust propagation-based [38] and inferencebased [96] models belong to this category.Golbeck et al. [38] proposed another trust inference method based on the FOAF concept that can assess which pairs of users trust each other and on which topic.Zhang and Yu [105] designed a semantic-based trust reasoning mechanism for trust prediction in OSNs.They inferred trust relations by designing a domain ontology and exploiting role-based and behavior-based reasoning functions [105].Liu et al. [62] proposed a heuristic model, called the Heuristic Social Context-Aware Trust Network Discovery algorithm, adopting the K-best-first search for addressing the trust network extraction problem by developing a contextual social network structure and proposing the concept of Quality of Trust Network [62].Parvin et al. [74] introduced a collaborative filtering recommender system based on ant colony optimization (ACO) algorithm and users' trust network.They ranked users and assigned proper weight values to users to identify the similarity levels among users.Jiang et al. [49] proposed a slope one algorithm with the help of trust data and user similarity to introduce a collaborating filtering-based recommender system.Forouzandeh et al. [29] introduced a recommender system that operates based on the users' behavior on Facebook and in two phases offers the users to buy their favorite products.Guo et al. [44] proposed a trust-aware recommender system based on a matrix factorization model.Their model focuses on item recommendation rather than rating prediction and also uses the trust values provided by explicit users' feedback.Azadjalal et al. [4] introduced a trust aware recommendation system and used trust values to improve the accuracy of their model in present of the sparsity of user-item ratings matrix.They proposed a model for identifying implicit trust relations and detected the most prominent users based on the Pareto dominance and confidence concepts to use their opinions in their recommendation model.Ghavipour et al. [36] introduced a trust inference model based on aggregation strategy and learning automata.Ruan et al. [81] introduced a trust inference model for OSNs using trust's transitivity property and developed a metric for measuring the trust level and its certainty.

& Hybrid Trust Prediction
These models combine the network-based and interaction-based models.In [92], the authors simultaneously considered users' previous interactions and the social network's structure.The authors of [34] proposed a trust prediction model called TDTrust; They introduced a set of context factors for capturing contexts of trust relations among users in OSNs; also mathematically modeled their trust prediction approach, based on threedimensional tensor decomposition to consider the context of trust directly in their model.In another study [35], the researchers introduced a new unsupervised approach, SETTrust, which incorporates the social exchange theory.Bo et al. [108] developed a trust link detection model; their purpose tens to find subjective trust, reputation, and indirect link between users; They calculated the subjective trust with the help of the users' previous interactions and determined the users' reputation based on collective objective trust.

Community detection algorithms
Finally, due to the importance of the first step of the proposed method a summary of community detection works on social network is provided below: Community detection is one of the most popular researches in a variety of systems, ranging from sociology to biology [46].There have been a huge number of algorithms and methods developed for community detection.Fortunato et al. [31] presented a comprehensive investigation thereof in 2010.There have been discussions of community detection algorithms of a variety of types along with the relevant graph types.Closely-linked groups are identified in the community detection problem, known as clusters, communities, or modules.The graph is divided in a partitioning-based method into components that contain fewer interconnections [52].Community detection algorithms have been designed most recently based on modularity.Based on edge-betweenness centrality, a clustering-based divisive algorithm was proposed by Girvan and Newman [37].The edge with the highest value of betweenness would be removed in each iteration.Biswas et al. [9] proposed the ENBC algorithm to model the community detection problem within the framework of human relationships.They used the notion of ego network, a novel network abstraction type considering personalized and the consequent mutual interests.ENBC was found to obtain proper trade-off between accuracy and quality.Biswas et al. [11] developed a mechanism of regression line dominance and shifting for community detection.They also considered convergence rate as well as solution quality to present a visual analysis approach to optimized transformed community detection.The same researchers proposed a fuzzy agglomerative method in [12] to use the membership degrees of all nodes for identification of the community structure of a network, giving all nodes fair chances of creating their personal communities, a notion introduced as self-membership.Communities could thus be detected naturally using an iterative algorithm.
The existing link prediction algorithms are compared in Table 1.

Proposed approach
The proposed method is composed of two steps.The trust communities are identified in the first step, and a trust route is found in the second step between the source and destination nodes over communities with the most significant trust.Initially, two nodes are selected as input; Through the best trust communities already listed, the best trust route between them is introduced, which includes a list of nodes with the highest trust value.
Various parameters are used to trust community detection (section 3-2, which includes Reputation, Mutual Trust, Common Trust, Kullback-Leibler distance, Similarity, Level Attenuation Rule, and Dependence).Upon provision of access to the datasets (the datasets used include Advogato, Adolescent Health, High School, Residence Hall, Slashdot Zoo, Epinions, Seventh Grader, Dutch College, Douban, Facebook, and Highland Tribes), the trust communities are obtained using the algorithm.All the information is stored in the database, including the trust communities, nodes in each community, average trust in each community, trust value of each node, and overlapping communities, along with a descending list of trust communities given their total mean trust values.Figure 1 shows the algorithm of the proposed method.
According to Fig. 1, in the first step, we detect the trust communities and store their information.Whenever necessary, with the help of this information and the list of trust communities, we find the trust route between two nodes of source and destination.
Step1: Trust Communities Detection A social network that includes nodes, the edges between them, and trust values is given as input.At first, each node is considered a single community.If the nodes are close to the desired conditions, this method continues to search and form communities based on the characteristic.A node remains in its community unless it deserves to join another community (high similarity).However, when there is not enough similarity between them, no association is formed between communities, and the situation is checked with another community.Different communities are created based on the similarity percentage with the specified characteristics.This process continues until the communities are dense, i.e., the highest internal and lowest external similarities among the communities.Thus,  Low accuracy Connection of a target node pair based on information theory [90] Robust & consistent

High theoretical complexity
Link prediction based on an intermediary network feature process [109] High scalability

-
The clustering coefficient of a common neighbor [98] High efficiency

Low accuracy
The TRA index, emphasizing the significance of the common neighbors [5] Low accuracy Assign a smaller weight to a longer path [51] Robust & consistent

-
The similarity score of a target pair of nodes based on that of their neighbors [47] Network structure constraint Use the paths of lengths 2 and 3 between two nodes to estimate their similarity [65] High robustness High scalability Network structure constraint Link prediction through logically linear embedding (LLE) [80] successfully in link prediction extremely complicate, hardly scalable in implementation Link prediction through Laplacian eigenmaps [8] successfully in link prediction // DeepWalk, a local embedding method using local information from random walks [77] High efficiency // Node2vec, used to embed the nodes in the representational space [42] Maximize co-occurrence likelihood of RW // Used combined machine learning algorithms and fuzzy logic [71] Used SVM, DT and kNN

Used only Epinions
Artificial Bee Colony (ABC) [83] Developed the best-fitted model -Link prediction based on community information Used information from within-cluster and inter-cluster shared neighbors [94] --WIC index compute the probability of connection of a node pair low speed Ranked Potential links within a community separately from ones between different communities [99] unconnected nodes are more likely to involve missing links -Using edge centrality along with community information in the community-based link prediction algorithm [10] computes edge centrality (EC) and community-based edge weight (CEW) for each of the existing links High time-complexity Using intra-community and inter-community information [14] Assigned links with ends within the same community positive weights -Proposing a community bridge boosting prediction model [32] enhance the similarity scores of bridge nodes.
Just to datasets: Epinions, FilmTrust using the generalized clustering coefficient for prediction of probability [45] A meta-heuristic method for obtaining a trust route, Proposing topology-based link prediction Comparison with only two methods and limited experimental scope Using resolution-based community division [24] distinguish different communities, and computed the probability scores of target links Ignoring information hidden between communities.
Used algebraic connectivity regularization [103] propose a one-step process

Method and Algorithm
Advantage Disadvantage Link prediction approach in generation of links and evolution of networks for diffusion of information [57] Predicted with efficient content spread [16] achievement of information relevance -Calculated the shortest path between users to have the most trusted users [7] Provide the right group of friends in clusters -

Trust prediction algorithms Trust Prediction based
on Interaction Developing a trust prediction approach centering on users' communication behavior and trust and propagation trust [1] Use more criteria

Low scalability
Focusing on the subjective trust values of connected users, based on their social interactions [82] propagating known trust values among peers in a trusted network using an ordinary least squares regression model [101] assess the characteristic similarity trust, interaction trust, and platform evaluation trust

Low robustness
Trust Prediction based on Graph Trust propagation-based [38] assess which pairs of users trust each other and on which topic.
fail to capture the actual interactions among members Inference based [96] Consistent fail to capture the actual interactions among members A semantic-based trust reasoning mechanism [105] Inferred trust relations by a domain ontology Insufficient operation of func.The Heuristic Social Context-Aware Trust Network Discovery algorithm [62] addressing the trust network extraction problem Network structure constraint ant colony optimization (ACO) algorithm [74] ranked users and identify the similarity levels among users Lack of criteria Slope one algorithm [49] Using trust data and user similarity

High theoretical complexity
Using a matrix factorization model [44] Focuses on item recommendation

Lack of criteria
Used these trust values [4] Improve the accuracy -Using aggregation strategy and learning automata [36] -Using trust's transitivity property [81] Increase the level of trust and certainty

High theoretical complexity
Used users' previous interactions [92] Considered the SN's structure Focus on fewer interconnections

Lack scalability
Introduced algorithms based on modularity and edge-betweenness centrality [37] Removing the edge with the highest value

Low accuracy
Proposed the ENBC algorithm [9] Found to obtain proper trade-off between accuracy and quality -Developed mechanism of regression line dominance and shifting [11] Solution quality -Use of fuzzy agglomerative method [12] Identify communities naturally Network structure constraint different communities are created and expanded based on the percentage of similarity; In this process, with the help of Reputation, Common Trust, Mutual Trust, and Kullback-Leibler criteria, detailed in Section 3-2, we expand and form communities.Finally, the obtained information is stored, which includes the number of communities, the amount of trust in each community, the nodes in each community, and the trust of each node.Step2: Trust Rout Prediction In the next step, we can find the trust route if required.We give the source and destination nodes as input to the algorithm.The algorithm is obliged to find the best trust route based on the information of the trusted communities that it already has, using criteria and formulas (1) to (8) for each node; The repeated use of the same criteria and their effectiveness in determining the trust route increases its accuracy compared to other methods.Finally, the selected route is given to us as an output.

Details of the method
Trusted communities are first identified and sorted based on their related trust information.Therefore, whenever two nodes enter the algorithm as input to determine the route between them, the proposed algorithm introduces the trust route between the two nodes of source and destination with the help of a list of communities with the highest trust.Once the source and destination nodes are selected, two possible cases exist for finding the trust route between them. 1) One or both of the nodes may not belong to the trust communities and are therefore removed from them as untrusted nodes.To resolve the issue, we begin from the source node and connect it to the closest community (examining whether or not the neighbors belong to the communities and going through the same procedure for the next level of neighbors if they do not until the closest community is reached).We do the same for the destination node.2) Both nodes belong to the trust communities, within which we seek a trust route between the nodes in the next step.We define thresholds for acceptance of the metrics (considering the network and the numbers of nodes, links, etc.), as exemplified below for the Advogato network: Reputation > =10.
Considering thresholds may cause multiple routes to be detected even if they differ in only one node.Attempts are made all along to select the shortest paths.If several trust routes are introduced finally, the level attenuation metric will be applied, based on which a longer route denotes attenuated trust.Therefore, a comparison is made between the introduced routes in terms of the number of steps and mean trust value.

Parameters
For identification of the trust communities and trust route, once a list of trust communities is stored along with their nodes and trust values, the following metrics are used to evaluate quality since the aim is to select still more trusted nodes from among the community nodes, to be added to the trust route list.

1.
Reputation.This metric is used to obtain the number of links input to a node and others' values of trust therein, i.e. examination of whether or not there is similar confident trust in a person.In which (trust in )n i indicates the value of trusted incoming links to n i and (link in )n i indicates incoming links to n i .
and consider number of link in .
2. Mutual Trust.This metric is used to examine if the two intended users trust each other directly and to specify the value if they do.If there is such trust, it will affect the two users' overall trust in each other [40].At the beginning, it is examined whether there is direct trust between the two users; if so, how much trust is there in the relation?If there is trust, this will have its own effect on the two users' trust in each other.Let the users d i and d j have trust degrees (d i , d j ) and (d j , d i ).The mutual trust factor can be calculated as: 3. Common Trust.This metric is used to examine whether the two intended users have common neighbors and high trust or not.In fact, if the users share a set of trusted users, there is high trust between them [40].Suppose that there are two individual d i and d j and that they have a set of common trust users Com = {cu 1 , cu 2 , ...}.For cu k ∈ Com, d i and d j have trust degrees trust (d i , cu k ) and trust (d j , cu k ), respectively.Then, the common trust factor of d i and d j is calculated as: 4. Kullback-Leibler distance.This is a non-parallel metric for measurement of the probability distributions of p and q based on probability theory and information theory [39].In general, p represents the actual distribution, and q is assumed to be an estimated value thereof.
5. Similarity.To predict the probability of friendship between i and j, it should be checked whether they have friends who are already friends with each other.In this case, the probability that they will become friends in the future will be higher than in the case where they have common friends who are not friends with each other.It is worth noting that the link prediction method will be more accurate and more efficient if the number of common neighbors c that have common neighbors themselves increases.A link prediction method based on similarity is therefore proposed.Moreover, this metric can be adapted via the network structure through consideration of −βC.The presented method is formulated as in the following equation [78]: where c is a common neighbor of nodes i and j, |Cc| is the number of neighbors of c consisting of the common neighbors of i and j including i and j themselves, |Nc| is the number of neighbors of c, C is average clustering coefficient, and β is a tunable constant value.6. Level Attenuation Rule.This metric is used to obtain the level of trusts, and seeks to reduce cost as much as possible by shortening the trust route.That is, the trust conveyed by the route is attenuated as the number of levels increases, that the longer the route, the cost and time of finding a route increases; it means the less valuable the conveyed trust in computation.
where parameter ζ ∈[0,1] is given in advance.If rt is on the first level, for instance, i.e. rs→rt (lev(rt) =1), the attenuation factor is 2 in this example).The trust in the serial route can then be calculated as follows: 7. Dependence.As nodes and communities are traversed to obtain the trust route, dependence is the most crucial feature that is considered besides the above metrics.Using this feature, a community with a more significant number of relations that are more trusted has a higher priority of selection.To increase the accuracy of link prediction among the trust communities, the power of the relations in the community is also considered, defined, and measured as a percentage for examining the community relations.On that basis, two communities with more relations and greater trust achieve more powerful relations; So, so the number of relations between them is considered besides their values of trust.Therefore, the dependence score between a community and itself is the highest.Since the dependence score represents the amount of interdependence between two communities, their similarity score is of great significance.The similarity scores of the nodes are reconsidered as follows in the proposed method.
The majority of the parameters used here have been described in detail in our earlier papers [39,40].In fact, all of the above metrics are used once to identify trust communities and once to find the trust route between the two selected nodes and between preselected trust communities, and all these steps serve to increase trust in the proposed route.Link prediction concerns the estimation of the probability that there is an unknown or a future link based on the available information.In this research, the probability that there is a relation between two target nodes depends not only on their individual features but also on the closeness of the associated trust communities.

Time complexity
As mentioned previously, the proposed algorithm is done in two steps.
Step 1: First, each node is considered a community, and its weight and reputation are calculated.A loop is formed in line 1 with a time complexity of n2.Given that the number of nodes in the graph is n, and the nodes have been checked before entering into the loop, the final number of loop iterations is n − 1.Within the loop, similarity, mutual trust, and common trust are calculated as long as the communities are merged.Each of them that is less than the others are better than them and therefore better-trusted, so it is selected for merging.The loop continues until all the communities reach density.Therefore, the complexity of the method proposed in this step is n 2 + n-1, in short O(n 2 ).
Step 2: Using for loop, moving between nodes is done for trusted route detection.The loop has n 2 complexity (line 7).Considering that the number of communities is n, and before entering the loop, a list of community information is available for review.Thus, loop repeating is at most n-1.Then Reputation, Mutual Trust, Common Trust, Level Attenuation Rule, and Dependence of nodes (line 8) are calculated.If route and node are not found between two communities, then nodes with a lower degree of trust to move between communities (line 9) are used; the worst-case scenario is when the route is not found, and we have to go through (n.(n-1)) times.Therefore, the complexity of this step is n 2 + n-1+ n 2 -n, namely O(n) 2 .Finally, the sum of the time complexity of these two steps is considered as the time complexity of the proposed algorithm; O(n) 2

Datasets
The following datasets are used for the experiments.All datasets are available on the sites konect.uni-koblenz.deand snap.stanford.edu(Table 2). 1.Advogato is a trust network set up in 1999, which is used by free software developers as the online community platform.Each Advogato user is represented by a node, and each trust relation is indicated by an edge.Known in Advogato as a certificate, a trust link consists of different edge weights, e.g.(1, 0.6, and 0.8).2. Adolescent Health was developed on the basis of a survey, where five best male and female friends were introduced by each student.Each student is indicated by a node, and each relation between two students is represented by an edge, where the student on the right has been selected as a friend by that on the left.The weight of an edge signifies the amount of interaction between the nodes, and unweighted edges denote absence of common activity.3. High School is a friendship network among boys in a small high school in Illinois, each subjected to the survey twice in Fall 1957 and Spring 1958.The results obtained in both periods were collected in the dataset.Each boy is indicated by a node, and each relation between two boys is represented by an edge, where the boy on the right has been selected as a friend by that on the left.The weight of an edge signifies the number of times the selection has been made.As a boy may have selected the same friend, the edge value ranges between 1 and 2. 4. Residence Hall involves ratings of friendship among 217 individuals residing in a place in the Australian National University, where each individual is indicated by a node, and each relation between two individuals is represented by an edge. 5. Slashdot Zoo is a social network composed of the relations between the users of the technology news website slashdot.org,listed as friend or enemy.The above labels are used there to mark users, affecting the scores viewed by each.For instance, if user A marks user B as enemy, the score of user B will be reduced according to user A. 6.Epinions is a network consisting of trust and distrust relations used on an online product rating website.It is composed of individual users connected by trust and distrust links.The edges are marked as +1 for trust or as −1 for distrust.Moreover, users can trust or distrust themselves, so the network involves loops.7. Seventh Grader is a network containing closeness ratings of 29 seventh-grade students of a school in Victoria.The students were asked to introduce their preferred classmates for three different activities.Each student is represented by a node, and each edge between two nodes indicates that the student on the left has selected that on the right as a preference.Edge weight ranges from 1 to 3, signifying the number of times the student on the left has selected that on the right as favorite.8. Dutch College is a network containing friendship ratings of 32 freshmen most of whom did not know each other before meeting at the university.Each student was asked to evaluate another at seven different points of time, with an uncertain origin but fixed distances.Each node represents a student, and each edge between two students indicates that the one on the left prefers that on the right.Edge weight signifies how well the node on the left finds the friendship, ranging from −1 for risk of clash to +3 for a best friend.Then, the proposed method was applied to the following undirected datasets for an extensive investigation.9. Douban is an undirected, unweighted social network used on a Chinese recommendation website.10.Facebook (NIPS) is a network composed of user-user Facebook friendships.Each node signifies a user, and each edge indicates a friendship relation between two users.11.Highland Tribes is the signed social network of the Gahuku-Gama alliance structure tribes residing in the eastern central highlands of New Guinea, from Kenneth Read (1954), composed of sixteen tribes connected by friendship and enmity, referred locally as rova and hina, respectively.

Evaluation metrics
The following parameters are used for the validation of the proposed method.To evaluate our method, we use popular criteria in evaluating the performance of algorithms.These parameters help us to accurately predict the number of trust links, explicit trust, and the quality of the ranked trust list by the tested algorithms; How integrated are the trust communities and trust paths obtained?Finally, we will also use a cost criterion to compare the results to see how much each algorithm can introduce shorter and less expensive routes.
1. Recall, precision, and F1.Prevalent in areas such as information retrieval, machine learning, and data mining, these are the metrics utilized to evaluate the performance of the algorithms.The recall parameter can be formulated as where TP represents the number of true positives, and FN indicates the number of false negatives.Here, the parameter denotes the ratio of the number of trust links predicted correctly by the algorithm to the number of them needing prediction.Precision can be formulated as follows: where FP represents the number of false positives.Here, the parameter denotes the ratio of the number of trust links predicted correctly by the algorithm to all the prediction results of the algorithm.F1 shows the harmonic mean of Precision and Recall, and ranging within [0, 1] can be formulated as: A higher value of each of the above three parameters denotes better algorithm performance [91].2. AR.This metric denotes mean high-ranking list loading in each query, mainly measuring the mean explicit trust percentage that can be identified through the obtained trust.
where N represents the number of testees, TN u indicates the set of users that are trusted explicitly by user U, and TL u denotes the trust list that is predicted for user U. A higher AR value, therefore, demonstrates an accurate prediction of users with greater explicit trust.3. NDCG.This metric concerns the normalized discounted cumulative gain, and measures the quality of the rated trust list.
where rel i is 1 if the user at position i is related and 0 otherwise.IDCG denotes ideal DCG, which is 1 where NDCG represents a perfect rating for a trust list of length n. 4. ATCE.This metric examines the integrity of community trust and the trust route.
where |C| represents the number of nodes in community C.An increase in the value of ATCE indicates higher community trust integrity.5. Cost.One of the criteria we used in this study was the level attenuation rule (Eq.6, 7), which aims to reduce costs by reducing the length of the trusted route.This means that the longer the route, the weaker the route trust, and the lower its value, so we tried to introduce shorter routes.During the comparisons, the length of the obtained routes was evaluated by a variety of selected methods, the methods that introduced a shorter route with a higher average trust were included in the list of low-cost methods.The results of experiments based on this criterion can be seen in Figs. 13, 14 and 15.

Hardware and software requirements
The proposed algorithm is programmed in MATLAB, experimental status of social networks has been implemented using R and Gephi software.Running on a computer using a 6 Cores CPU and a NVIDIA GeForce GTX 1080 12GB Graphics Processing Unit.

Compared methods
The proposed method is compared here with several state-of-the-art algorithms in the area of trust route prediction (Table 3).

Link prediction for directed and undirected networks
Here is a list of link prediction methods that can be used over both directed and undirected networks.
1. RSTN: In this method, to achieve better results, the suitable group of friends is clustered and the shortest path is calculated as well as the correlations among users and items.
Friendships and tags are combined as regularization terms to constrain the matrix factorization framework.The users are clustered to obtain suitable groups of friends, then the shortest path between users is calculated to have the most trusted users [7].Bridge-based method with CN indexing the basic similarity [32] E q .( 24) AA_B Bridge-based method with AA indexing the basic similarity [32] E q .( 24) RA_B Bridge-based method with RA indexing the basic similarity [32] E q .( 24) 2. ABC: This Method is organized in two phases: the first phase deals with distinguishing the trust between any two users of a social network, and the second phase proposes a meta-heuristic method for obtaining a trust route based on the result of the first phase [83].3. Katz.This method enumerates the possible paths between two nodes, and exponentially discounts the longer ones.Let path l ij be the set of all paths of length l from node i to node j.Given a weight 0 < β < 1, the Katz score is: 4. RS.This is a method of rating pairs of users based on the similarity of their ratings.
Moreover, the following prediction methods are used in the experiments for comparison. 5. CN [72], AA [2], and RA [111] are three conventional similarity indices.The CN index obtains the score of similarity of the two target nodes by counting the common neighbors [72], and the AA and RA indices consider the influence of common neighbors with high degrees to discriminate the participation by different common neighbors.
Ω xy represents the number of common neighbors of x and y. k z indicates the degree of node z. 6. CAR [15] is an index that connects local community links to CN.Similarly, CAA and CRA connect these links to AA and RA, respectively.
L(z) is the number of links between z and other common neighbors of x and y.
7. WIC [94] detects lost links based on information on the community structure and Bayes' theorem.According to Gao's model, bridge nodes, which connect several communities, are likely to generate new links.Therefore, the similarity scores of bridges will be enhanced if they double [32].
In WIC, δ is a very small constant value.Here, it is set to δ = 0.001.8. CN_B, AA_B, and RA_B are three bridge-based methods of prediction proposed in this research, where the basic similarity is indexed by CN, AA, and RA, respectively.
Ω xy represents the number of common neighbors of x and y.Ω W xy denotes the set of common neighbors that lie in the same community as x and y.

Results and discussion
For a better analysis, the precision of the proposed method was compared to that of the other selected algorithms.For a preliminary evaluation, comparisons were made over the eight directed networks using all the above methods, as shown in Figs. 2 and 3, and also on the four undirected datasets that can be seen in Fig. 4 Fig. 2 A comparison of the proposed method in terms of Precision over the first four datasets In Figs. 2 and 3, the precision of the proposed TRTCD method is investigated with 14 other methods on eight directed datasets.The results show that the proposed method can work well on selected datasets.The RSTN and ABC methods also gave good results because the RSTN method introduces the most reliable users by clustering and calculating the shortest path between users.ABC proposes a meta-heuristic for obtaining a trust route, and both of these methods were able to predict the path.However, in contrast, two methods, CN and RS, compared to other methods, could not achieve acceptable accuracy on all datasets because RS and CN determine the similarity points between the two target nodes and find the trusted links, respectively, through the similarity of user rankings and counting common neighbors.The results showed that these methods do not significantly increase the quality of detection of trusted routes.Similarly, in the following, comparisons based on precision criteria are performed on undirected networks, which are shown in Fig. 4 Fig. 3 A comparison of the proposed method in terms of Precision over the second four datasets Fig. 4 A comparison of the proposed method in terms of Precision over the three undirected datasets Figure 4 shows the performance of the proposed method on the undirected networks, where the Precision of the proposed method is slightly lower than that of the others, indicating its poor performance over this type of networks.
As can be seen from the diagrams and results of Figs. 2, 3, and 4, the proposed method works well on directed datasets compared to other methods while it does not have good precision in three undirected networks; that is because in these networks some parameters are not used, such as the criterion of mutual trust or common trust; meanwhile, since the links are unweighted, for example, mutual trust is meaningless here.Of course, compared to the other methods selected in this paper, it also performs acceptable in undirected networks, but in general, it has lower precision compared to eight directed networks.
In the following, comparisons will be made in terms of Recall criteria, the results of this evaluation are shown for eight directed datasets in Figs. 5, 6, and three undirected datasets in Fig. 7.
Examination of the proposed method in terms of F1 criteria is also shown in Figs. 8, 9 and 10.Figures 5, 6 and 7 show comparisons in terms of Recall over the directed and undirected datasets, where the proposed method obtained proper results as compared to the other fourteen methods over the directed datasets.In undirected ones, due to the existence of values of trust and its use in calculations, our proposed method does not have a significant advantage.The basis of our method is the trust values between the nodes, since these values do not exist in the undirected datasets, our method did not have good results.This is also true for the F1 metric based on Figs. 8, 9 and 10.Figures 8, 9 and 10 show the evaluation results of the proposed method according to the F1 criterion.Considering the comparisons of precision and Recall, the results of this criterion can be understood to some extent; because F1 indicates the harmonic mean of precision and recall, the higher the value of each of the precision and recall parameters, the better the performance of this criterion and algorithm.In comparisons made on undirected datasets, the proposed method, unfortunately, did not achieve good results.The reason for the low efficiency of the method presented in these three datasets is that the proposed method performs based on the information of each node and community, while these three datasets cannot provide this Fig. 5 A comparison of the proposed method in terms of Recall over the first four datasets information and do not have any required information and values of links and communities.They can only show the minimum relationship between nodes, which is not enough for our proposed algorithm.Therefore, it causes lack of quality in introducing trusted routes.comparison based on AR metric is given in Table 4.This criterion measures the average percentage of explicit trust that can be identified through trust.Thus, a higher AR value indicates the accurate prediction of users with more explicit trust.
In Table 4, the mean explicit trust of the proposed method was measured using the AR criterion.As it turns out, with the help of the proposed method, we were able to achieve a higher average of explicit trust.This means that it can be clearly stated that the average values of trust in the trust routs of the proposed method are higher than other methods.This criterion was examined on undirected datasets, but we did not achieve high accuracy; this is because the Fig. 6 A comparison of the proposed method in terms of Recall over the second four datasets basis of the proposed method is the trust values of the links between the nodes and their direction.
Comparisons were then made between the methods in terms of ATCE for examination of integrity in community trust and the trust route.
We decided to perform just one experiment on the first part of the proposed algorithm, which is community detection, to see how good it is.Figure 11, shows the experimental results of our proposed method and TLCDA [17], Infomap, Eigenvector, CNM (Clauset-Newman-Moore) [19], and GN [37] methods.The purpose of all these algorithms is to detect communities on social networks.Eigenvector detects communities toward modularity optimization, and the obtained community structure thus usually exhibits far higher modularity [17].Infomap is a community detection algorithm that is based on the principles of information Fig. 8 A comparison of the proposed method in terms of F1 over the first four datasets transmission in the network.When a variety of communities in the network are considerably different in scale, Infomap is preferable to the modularity optimization algorithm.The purpose of this comparison is to evaluate the integration of all six methods on directed datasets.For this experiment, different numbers of communities are created each time, from one to twenty communities.Experiments are repeated 20 times to evaluate the degree of integration of communities in different methods on each network, and the average values are plotted.These five methods were chosen for this comparison because of all them are community detection methods in social networks.
It was observed that the proposed method performed better than other algorithms in terms of ATCE metric, because more integrated communities were identified.The largest ATCE after the proposed method was obtained by TLCDA algorithm and the smallest ATCE was obtained by Infomap.The proposed method performed better than TLCDA, Infomap, Eigenvector, CNM, and GN methods with values of 0.32, 1.93, 1.79, 1.22, and 1.06%, respectively.
In Fig. 12, we want to show the performance of the proposed method in terms of NDCG metric.NDCG measures the quality of the trusted rating list.In fact, NDCG represents a good score for a trust list of length n.
In this review, we will compare the average trusted list of trust routs displayed in the output of our work with the output of the other methods.In the proposed method, one of the values that appears in the output is the list of trusted routes in addition to the average trust of the entire route; Therefore, the average trust can be compared to see whether the proposed method was able to obtain a higher value in the list of trusted routes or not.
In Fig. 12, the NDCG criterion was used to evaluate the quality of the list of trust routs obtained in the selected methods.This measure is in the range of 0 to 1.The results showed that the average value of trust for the proposed method is very close to 1.The NDCG values for RSTN, ABC, RA_B and AA_B are about 0.9 and higher than other methods.CRA, CAA, CN_B and WIC have better trusted route lists in the next categories.
In the last comparison, we want to examine the cost criterion on the selected methods.The results of these comparisons are shown in Figs. 13, 14 and 15.In Figs. 13 and 14, the proposed method was compared to fourteen methods in terms of cost.According to the experiments performed on the eight directed datasets, the proposed method performed slightly better than the others.However, the results of RSTN, ABC are very close to the proposed method and some other methods such as CN_B, AA_B, and RA_B have slightly higher cost than the proposed method, in discovering trust route.The introduction of the route in these three methods is based on the bridge, which accelerates the detection process and ultimately reduces costs.
Figure 15 compares the proposed method and the other selected methods in terms of Cost.The experiment was performed on three undirected datasets.Due to the decrement in the effect of the parameter on the search for the trust route and trust communities, there was lower Cost in general in all the methods.However, the proposed method exhibited lower cost than the  We also measured the cost criterion on undirected social networks to determine the quality of the routes obtained.One of the factors that showed the proposed method could not achieve good results in undirected social networks was the cost criterion, and it was much more expensive to find trust routes compared to other methods.This shows that the proposed criteria are unsuitable for undirected social networks because it introduces longer routes with lower trust.
The limitations of the current study The limitation of our work was the use of undirected datasets to test and check the quality of the proposed algorithm.We used three undirected datasets of Douban, Facebook, and Highland tribes.The proposed method in these networks cannot find the trust paths because the parameters we use, including Mutual Trust, Reputation,   Therefore, in this data set, some parameters could be more effective.

Conclusion and future works
In any social network, users worry about not having trusted relationships and losing their privacy because each user's priority is to communicate with people they can trust to avoid being easily deceived by untrustworthy people.Therefore, to achieve this goal, by presenting a new method in this article, we identified the paths of trust between users using the trust values of social network nodes and trust communities created to reduce the fear of losing people's privacy as possible.For this purpose, in the first stage, trust communities were identified.In the second stage, a trust route was created between the source and destination nodes in the communities with the most trust, using several metrics (Reputation, Mutual Trust, Common Trust, Kullback-Leibler distance, Similarity, Level Attenuation Rule, and Dependence) at the same time for the identification of trust communities and trust routs.Finally, through the previously listed best trust communities, we introduced the best trust path between them, which includes the list of nodes with the highest trust value.To evaluate the performance of our proposed method, TRTCD, we compared it to several popular methods of link prediction both on directed and undirected networks Advogato, Adolescent Health, High School, Residence Hall, Slashdot Zoo, Epinions, Seventh Grader, Dutch College, Douban, Facebook and Highland Tribes.
As is clear from the results of the experiments, the proposed method achieved high precision in the search for trust paths over the datasets, according to Figs. 2 and 3, in directional networks.According to Figs. 5 and 6 and 8-9, the proposed method obtained good results compared to fourteen other methods in the directed dataset regarding Recall and F1.The results show that with the help of the proposed method, a higher average of explicit trust can be achieved, and it can be clearly stated that the average values of trust in the trust paths of the proposed method are higher than other methods.Also, with the help of the proposed method, we achieved a higher average of explicit trust (AR criterion).This means that it can be clearly stated that the average values of trust in the trust routes of our method are higher than other methods.However, we did not achieve high accuracy in the undirected datasets.When the same comparisons were made on three undirected datasets: Douban, Facebook, and Highland tribes, the proposed method could not find the trust routs in these networks well and accurately; this is because in these datasets, some parameters have no effect and cannot be very practical and helpful, such as Reputation, Mutual Trust, and Common Trust criteria, because links have no weight and there are no trust values.Also, according to the experimental results, the proposed method could not achieve good results in terms of cost criteria in undirected social networks.Because finding trust routes with the help of the proposed method was much more expensive than other methods, and that is due to the need for more clarity in our criteria for undirected social networks.
Therefore, future work is to focus on this issue; by considering more criteria, including Closeness, Triadic Closure, Betweenness, Homophily, and so on, in addition to directed social networks, we can also extend the issue of trust to undirected social networks and increase the quality and accuracy on these networks.
Score of similarity of two target nodes as the product of their degrees [72] --CN High efficiency & scalability Low number of indicators Normalization of the results obtained by CN through the Jaccard coefficient [60] High robustness High theoretical complexity Normalization of the results obtained by CN through Hup Promoted index [79] Network structure constraint Normalization of the results obtained by CN through Hup Depressed index [111] -RA Robust & consistent High theoretical complexity Normalization of the results obtained by CN through local Leicht-Holme-Newman index [53] similarity proportional to the number of paths Network structure constraint Penalize the impacts of common neighbors with large degrees by the AA [2] -AA High robustness -Connection of a target node pair based on the Bayesian theory [61] Introduced a trust prediction model called TDTrust based on three-dimensional tensor decomposition [34] Introduced a set of context factors Low accuracy Introduced a new unsupervised approach, SETTrust [35] Taking advantage of social exchange theory Network structure constraint Finding subjective trust, reputation, and indirect link between users [108] Determined the users' reputation -Community detection algorithms Presented a comprehensive investigation thereof com.Detection [31] --survey Discussions type of com.detection algorithms -Used partitioning-based method [52]

A
Fig. 12 Comparison based on NDCG criteria in directed networks

2 S
Fig. 14 A comparison of the existing methods in terms of Cost over the second four datasets

Fig. 13 A
Fig. 13 A comparison of the existing methods in terms of Cost over the first four datasets

Fig. 15 A
Fig. 15 A comparison of the existing methods in terms of Cost over the three undirected datasets

Table 1
A summary of related papers Category

Table 2
Information
F1TRTCD RSTN ABC Katz RS CN AA RA CAR CAA CRA WIC CN_B AA_B RA_B Fig.10A comparison of the proposed method in terms of F1 over the three undirected datasets COSTTRTCD RSTN ABC Katz RS CN AA RA CAR CAA CRA WIC CN_B AA_B RA_B