2.1 Event Logs

Event data is a type of dark data [74]. Regarding the business process management perspective, event data is related to the execution of a particular business process, and it is recorded in a wide variety of data sources such as databases, flat files, message logs, transaction logs, enterprise resource planning (ERP) systems and document management systems. Each event refers to a particular activity. An activity is a well-defined step in the business process. Each event can be recorded with extra information such as executive resource (e.g., person, device, machine or computer servers), initiator of the activity, time label or other recorded data factors in the event (e.g., the execution place of activity) [5]. Consequently, doing any activity can lead to record an event. The activities are not only limited to the business processes. From a systemic perspective, web or mobile application systems (e.g., social networks) also include a set of activities. Messaging, sharing content, commenting, etc. are among the possible activities on social networks [48]. A fragment of event logs is displayed in table 1. An event (Pid, a, r, t) describes something happened during the execution of a specific business process P [85]. It is characterized by a set of mandatory characteristics. They have written in the header row of table 1.

Table 1: A fragment of event logs 

2.2 Conformance Checking

Process mining has been introduced since 2012 as an integral part of data science, which was constructed by event data [83], [87]. Techniques, tools and process mining methods could extract knowledge from event logs which usually exist in today's information systems [87]. Knowledge extraction leads to understanding the behaviour of individuals, organizations, machines, and systems [83]. The benefits of the process mining come from several different viewpoints [6], [75], [87]: control flow perspective, executive perspective, organizational perspective, and case. One of the important issues in all approaches of process mining is conformance checking. Conformance checking has been mostly studied from the control flow viewpoint [3], [7], [75], [85], [87], [96].

One of the important goals in business process management (consequently, process mining) is conformance checking. Conformance checking compares the model extracted from the event logs with the primary default model [85]. From the control flow viewpoint, the model is a business process model or workflow model. In this model, the priority of activities and their logical connection are determined. For instance, there may be a process model indicating that purchase orders of more than one million Euro require two checks. Analysis of the event logs will show whether this rule is followed or not. Another example is the checking of the so-called four-eyes principle stating that particular activities should not be executed by one and the same person. By scanning the event logs using a model specifying these requirements, one can discover potential cases of fraud. Hence, conformance checking may be used to detect, locate and explain deviations, and to measure the severity of these deviations [85]. Some studies with this approach are discussed here.

Rozinat and van der Aalst examined the matching of the business process model and event logs in process-aware information systems. They developed a matching checker in the ProM framework [70]. van der Aalst and de Medeiros advocated the use of process mining techniques (Alpha algorithm) to detect anomalous process executions and check process conformance [88]. Furthermore, Accorsi and Stocker used conformance checking with the control flow viewpoint for security audits [1].

The author in [86] identified two ways to create and/or maintain the fit between business processes and supporting information systems: delta analysis and conformance testing. Delta analysis compares the discovered model with some predefined processes model. Conformance testing attempts to quantify the fit between the event logs and some predefined processes model. van der Aalst et. al studied the behaviour of the web services through conformance checking. Their study addresses the problem of checking and quantifying how much the actual behaviour of a web service, as recorded in event logs, conforms to the expected behaviour as specified in a process model [89]. In recent years, other similar studies also performed conformance checking regard to process model discovery aspect [16], [51], [79], [92].

While the conformance checking is not limited to control flow [85], [101], so far, the conformance checking has been studied from the perspective of the control flow viewpoint [3], [7], [16], [51], [75], [79], [83], [85], [92], [96]. In organizational mining, the model can be an organizational structure [84], [86]. The resources interactions in the event logs can be mapped to a network based on the handover of works scenario and its conformity to the organizational structure can be investigated. Although some studies have used the old clustering methods to explore the organizational structure [2], [31], [53], [75], [90], none of them have focused on conformance checking.

In this research, we seek to find a structured and meaningful relationship between the social network and the human resources' interactions network in the context of social commerce. To this end, while modeling the problem with the multi-layered network, we employ the concepts and methods of link prediction and triadic closure. Conformance checking between the two networks (social network and activity network), and also using statistical analysis fulfills our goal and confirms our approach. Accordingly, some of our research differences in the problem domain are:

- Conformance checking studies have so far been addressed in the context of information systems and web services interactions, and have not been used in other areas such as electronic commerce and social commerce. The study of social commerce systems differs from that of information systems. Social commerce is the evolution of e-commerce, which includes both business and social activities together [10], [24], [39]. Therefore, while information systems in the organization are analyzed only based on the information flow, in social commerce systems there is not only information flow but also there are financial and goods/services flows and can be analyzed [9], [68]. Social relations are also available in these systems [11], [34]. Hence, it is possible to examine each of the flows independently and all three flows together with social relations; studying them can create a complete understanding of the various dimensions of the business.

- Previous studies have focused on conformance checking from the control flow point of view, while it can be investigated from the organizational viewpoint and based on the relations among process resources [85]. Therefore, by considering the impact of social relations on business interactions and people's co-operation [38], [58], [67], the initial model in conformance checking can be the structure of human resources' social relations (or any structure based on formal relations such as organizational structure or informal relations like a friendship network). As a result, the matching of business interactions among human resources in the event logs is compared to that of the initial model, and vice versa. In this research, we are looking for this objective.

Consideration of the mentioned differences in the problem domain, for the following reasons we can not employ the approaches of conformance checking that are proposed in process model discovery studies. Conformance checking in the process model approach is performed between the process model discovered from the event log and the initial process model [16], [51], [70], [79], [85], [92]. A process involves a set of tasks that between every two tasks exists a logical link [86]. The event log is generated based on the structure of the initial process. A discovered process model which generates an event log that is similar to the event log of the initial model is appropriate. Also, the initial model’s event log should be tracked by the discovered model (see the conformance checking metrics in [16], [51], [79], and [92]). Therefore, the input of these methods is the event log, and their output is the process model discovered from the event log. Finally, the conformance rate is reported based on the evaluation metrics.

In this research, equivalent to the process model, we have a network of social relations among human resources. But the logical structure does not govern social relations. On the other hand, there is a process which makes some interactions among human resources, and the execution of the process is stored in the event log indirectly. We aim to study the influence of the social relations network on the execution of the process and, in particular, we seek to know how the work interactions form among human resources. Thus, regards to the goal of this research, we do not discover the process model or organizational structure from the event logs. Hence, the methods and approaches of previous studies that focus on discovering a process model or discovering an organizational structure are not effective in our research. In our study, the input is the event log and the social relations network. These two are from two separate contexts. We also have two outputs. 1) The intermediate output includes the activity network extracted from the event logs and the activity network generated based on social relations. The second activity network is based on methods and concepts of social network analysis. Activity networks consist of human resources. Both human resources are linked to each other based on the activities they have performed. As a result, activity network is different from the process model. 2) The final output which is the values of the conformance of the activity network and the network of social relations. Therefore, the methods used in the process model discovery researches are not appropriate for our research.

2.3 Activity Network

The term network activity is also used in researches on social network analysis. An activity network in social network analysis is a result of activities that users do in social network sites. For example, commenting, liking, following and so on. In fact, the activity network in the social networks domain includes users as nodes and what they do in their interactions, is an edge [8], [20], [44], [48], [72]. For example, if user 𝐴 sends a message to user 𝐵, a directional edge is defined from 𝐴 to 𝐵. Usually, the activity network is a directed weighted network in social network analysis researches. But in general, the type of activity network depends on its construction scenario [48].

In researches of social network analysis, the activity network has not formed based on the business process. In other words, there is no assumption that the interactions among users on social networks are purposeful. Most researchers have structurally compared the network of users' friendships with users' activity network; for example, network evolution, degree distribution, degree correlation, the strength of relations, etc. Some also compare the characteristics of two networks over time. Khadangi has summarized these studies in [48]. For more information, refer to his study.

The activity network is formed based on one/several processes in our research; the process which is predefined or can be ad-hoc. Therefore, a set of rules governs it. For example, the tasks that a human resource can do is limited and specified. That is, the resource can not do all the tasks in the business context. The activity network can be extracted from the event logs according to different scenarios (see Section 3.1). In the previous researches, the term "sociogram" [91] was used instead of the activity network. But in this research there is also the network of social relations, so we used the activity network term to avoid confusion. Also, since relations among nodes are based on activities that human resources have done in the business process, the term activity network is more appropriate than sociogram.

To the best of our knowledge and review of process mining studies, there has been no research on the study of the relationship between social relations and activity network so far, and we believe this study is the first one.

3.1 Social Network Analysis

Social network analysis (SNA) or graph mining explores the social relations and network structures concerning graph theory. Social network analysis includes methods and metrics to extract information and knowledge from network structures. According to the graph theory, a single-layered network SN = (V,E) is formed by a not-null set of vertices (V) (i.e., members or actors) and a set of edges (E) (i.e., homogeneous relationships) which indicates an explicit or implicit relationship between two vertices [99]. Sets 𝑉 and 𝐸 are defined based on a scenario. Defining different scenarios to generate a network leads to the formation of different types of networks [28]. For example, the set of vertices can be defined as the resources of a process and the set of edges could be determined based on the handover of work. After the extraction of network from the event logs (e.g., based on the handover of work, joint activity, working together, etc. [90], [91]), analysis of the network based on the NA methods and metrics could be accomplished.

Since the social network analysis is based on the graph theory, and the graphs are categorized according to the features of the vertices and edges, the network extracted from the event logs could be varied as well (figure 1). Usually, the derived network based on the event logs is a graph with weighted and directed edges if the edges define based on the handover of works. The weight of each edge is equivalent to the frequency of occurrence of that edge. This graph has the homogeneous relationships with one type (e.g., the handover of work) and due to the existence of one vertex type (e.g., resources), it is considered as a one-mode network. When the edges are defined based on working together or joint activity, the graph will be undirected but can be weighted. Regards to figure 1 (a), Pete refers a case to Sara. Thus, a directed edge has drawn among them. In figure 1 (b), Pete and Mike have an edge since they do one joint activity entitled with registration request. Likewise, in figure 1 (c), due to the collaboration among Pete, Sara, and Mike for Pid = 1, these three persons are connected.

These social networks are named sociogram in other studies [91]. In this research, we denominate them activity network (see section 5.1). The tools such as Prom, NetMiner, and USINET have been employed hitherto in the research to analyze the networks extracted from the event logs.

Figure 1: Extracted networks based on different scenarios for event logs in table 1 (The grey node is an inhuman resource) 

Applying metrics and methods of NA, one can compare the individuals, organizations, and communications. These metrics are divided into two main categories: 1) micro-level metrics, i.e., metrics that examine only one specific node and 2) macro-level metrics, i.e., metrics that analyze the entire network.

Micro-level metrics: the role and effect of a specific vertex could be determined based on the metrics of micro-level. For instance, it could be figured out whether a vertex has the leadership role or it is only an isolated node relative to the entire network; whether a node is a bridge for connecting two key nodes or not [4]. Some of the important micro-level metrics include degree centrality (in-degree and out-degree), betweenness centrality [4], [75], closeness centrality (in closeness and out closeness), eigenvector centrality [4], and clustering coefficient. Each one of the given metrics is interpreted according to the application context. We have employed degree centrality metric in this research. It is defined as the number of links incident upon a node (i.e., the number of ties that a node has) [99]. In figure 1 (b) the degree centrality of node Mike is two.

Macro-level metrics: macro-level metrics provide insight and understanding of the overall network structure. These metrics include component, density, clustering coefficient, and centrality. Each metric has a different interpretation depending on the application context. For example, as there are fewer central nodes in the network, it will lead to increase the network centrality. One or a few of nodes administrate the network with high centrality. Therefore, if because of any reason this node is removed from the network, the network is divided into some disconnected sub-networks. The network with high centrality is not a good sign owing to all the credit and power of the network is accumulated in one person. In this research, the metrics of the component, density, and clustering coefficient are used.

In an unconnected graph, each connected part of the graph is called a component [99]. Furthermore, in an undirected simple graph, the density is defined as the ratio of the number of edges of the graph to the number of possible edges among nodes [99]. The clustering coefficient is defined based on triplets of nodes. A triplet is three nodes that are connected by either two (open triplet) or three (closed triplet) ties. The clustering coefficient is equal to the ratio of the number of closed triplets to the total number of triplets (open and closed triplets) [27], [95]. Nodes in a graph with a high clustering coefficient have more tendency to form clusters or communities.

Multi-layered Network

There is not always one type of relation (E) among the vertices (V) of a network. For example, there may be three types of relations within a network in which nodes are individuals: friendship, cooperation, and fellow-citizen. Modeling such a network can be done in two ways. The first is to weigh each of the relations (weights of the edges can be equal or different), then we define a simple network with weighted edges (the weight of each edge is equal to the total weights of each type of edges). Obviously, in this situation, the type of relation cannot be determined using the weight of the edges. Therefore, the reality is not fully modeled and the analysis may not be accurate. The second method is to consider each relationship as a simple network. Consequently, the network is represented as three simple networks or, in other words, a 3-layered network [23], [47]. In such a case, there may be differences between the vertices that exist on each layer with the vertices of the other layers. Also, depending on the application field, there may be edges between the vertices in two different layers [23]. Figure 2 shows an example of two modeling methods. There are no edges among different layers in this example.

Figure 2: A sample of two types of network modeling 

3.2 Statistical Analysis

Many natural phenomena, systems, and algorithms are inherently random in various fields. Examples of these areas include social processes, image processing, signal processing, information theory, computer science, and social sciences [15], [22]. For example, publishing a Tweet on the Twitter social network has an inherently random mechanism [46] and it depends on the probability of occurrence of some events. Also, by changing the probability, the propagation process may change. Therefore, statistical analysis is required when a phenomenon is random [25].

Nonparametric statistical methods are statistical methods used to determine whether a random phenomenon has occurred based on an accident or a chance. In fact, these methods determine whether a phenomenon has occurred based on a non-chance and meaningful pattern or behaviour [64]. Nonparametric statistical tests or nonparametric hypothesis tests are divided into two classes: pairwise comparison and multiple comparisons [25]. The pairwise comparison is a comparison between the two algorithms (e.g., the Wilcoxon Signed Rank Test [64]), while the multiple comparisons compare more than two algorithms (e.g., the nonparametric Friedman test [64]). More information on nonparametric statistical tests is available in [25].

Similar to nonparametric test methods, some statistical measures are used in social network analysis to identify frequent patterns (i.e., motifs). Two z-score and p-value measures are applied to identify motifs. The pattern with the higher z-score and the lower p-value is the more important one [35], [45], [49], [66], [69]. Indeed, it confirms that this pattern is a meaningful pattern and is not formed randomly or by chance.

In this regard, in this paper, Friedman's famous nonparametric test is employed to confirm the validity of the research hypothesis using the proposed conformance checking method.

5.1 Proposed Framework

The proposed framework of our model is drawn in figure 4. Function f has three sub-functions in the proposed framework: pre-processor, structural conformance checker, and behavioural conformance checker. Each function is explained in the following.

5.1.1 Pre-processor (SF1)

According to Definition 1, the human resources social relations (i.e., network SN ) have a graph-based structure. This is while the event logs do not have a graph-based structure. As a result, according to research questions, the interactions among human resources recorded in event logs should be mapped to a graph-based structure. Consequently, the two graph structures are comparable. In fact, we can check the conformation between the social network SN and the human resources interactions network (i.e., activity network) which is based on EventLog . Activity network can be created based on different scenarios from the event logs. Due to the social network is an undirected network, a scenario for constructing activity network should be selected to create an undirected network. Therefore, the two networks will have comparison conditions. Scenarios of working together and joint activities create an undirected activity network [5], [31], [75], [77], [91]. Since the roles and workgroups of each resource are not specific, a scenario is required to identify the clusters of the role or workgroup of each resource. Thus, the scenario of joint activities is the most appropriate scenario in our problem.

Definition 3: According to the multi-layered network definition 23, 48, AN _L = (V _anl ,E _anl ,L) is defined as a multi-layered, static, undirected and weighed activity network. L is the same set of flow type in EventLog. In other words, it specifies the interaction type among resources. Its values include L ={i,g,f}, when the value of index L is not set, all three values of L are considered. V _anl is a set of human resources in one of the layers of set L, and we have V _anl ⊂ V _SN and V _anl ⊂ r (in other words V _SN ∩R = V _AN and V _SN n V _{AN ≠} ??). E _anl e v _anl x V _anl is a set of relations based on the joint activities among the human resources in one of the layers of set L. As an example, there is an edge between two vertices 𝑖 and 𝑗 in the network AN _g when nodes 𝑖 and 𝑗 at least have one same activity like A _n in various executions of business processes, in a way that the activity A _n is accompanied by goods exchange between nodes 𝑖 and 𝑗. If financial transactions are carried out electronically, there may be no flow type f among human resources. Network AN _L is constructed through P01 in figure 4.

Therefore, a link is formed between two vertices i and 𝑗 at AN _L when these two vertices have carried out one same activity at least in one of the layers of set L. Two vertices 𝑖 and 𝑗 do the same activity due to they have the same role. Each role includes a set of legitimate activities. On the other hand, when the vertices 𝑖 and 𝑗 have a link in one of the layers of network AN _L , it means that a single human resource has referred the work to them or two different human resources with the same role have referred the work to the vertices 𝑖 and 𝑗. The number of joint activities between 𝑖 and 𝑗 is defined as the weight for their relationship.

Due to all persons in network SN do not exist in network AN _L , filtering the network AN _L based on the network SN is necessary for computing reduction.

Figure 4: The proposed framework of the conformance checking based on the multi-layered networks 

Definition 4: regarding the mentioned definitions, SN _’L = (V _sn’l’ , E _sn’L ) is defined as a static, undirected and unweighted social network in a way that SN _’L is a sub-graph of SN. V _sn’l is a subset of V _SN , and it is a set of people who exist in network AN _L and their friends. Likewise, E _sn’l ⊆ v _sn > _l x V _sn’l is a set of friendship relationships among individuals. Network SN _’L is constructed by P02 in figure 4.

5.1.2 Structural Conformance Checker (SF2)

In response to research questions, two networks 𝑆𝑁_𝐿 and AN _L are examined and compared from different structural aspects. For this purpose, the basic metrics of social network analysis and some of the concepts of social science are applied. Structural conformance involves structural features of the network, homophily, social role (popularity), and link dependency. We will explain them in more detail. In Figure 4, P03 performs structural conformance checking calculations based on the NetworkX library in Python and VBA in Excel. Finally, P04 maps out charts and graphs.

Network structural characteristics: The structural characteristics of the network, are the main features that the network structure is defined by that. These features include the number of vertices\ V\, the number of edges \E\, type of vertices, type of edges, density D, number of connected components #CC, graph clustering coefficient GCC, and degree distribution. For each equal value of the features in networks AN _L and SN' _L , a value True is added to set X.

Homophily: Homophily principle [50] proves that people with similar characteristics (e.g., social situation, age and so on) tend to work together. Especially, we study the link homophily. We examine whether two people (human resource) who have mutual friendship edges in network SN' _L , will tend to collaborate with each other in network AN _L . Is having more common friends in SN' _L, equivalent to have a relationship in the network AN _L ? The answer to these questions is examined for different flows. If there is a linear relationship between the number of mutual friends and the probability of connection, value True will add to set X.

Popularity: To the popularity, we investigate whether two popular individuals in social network 𝑆𝑁 𝐿 ′ are connected to each other in the activity network AN _L or not? If more than 10 percent of relations are based on the popularity, True as another value will add to set X. Degree centrality is applied for measuring popularity [81]. The popular person has defined in a way that his/her degree centrality is among the top 10 percent ones. The other individuals are ordinary. 2-bit binary codes (XX) (X = 0 or 1) are employed to represent the dual status. Zero means an ordinary person and 1 denotes a popular one. Likewise, popularity status is determined based on the network SN' _L , and the links are checked in the network AN _L for each different flow. As an example, how much is the probability of linking in network 𝐴𝑁_𝑖 for status 11? Owing to the networks are undirected, there are three status of 00, 11 and 10 or 01.

Link dependency: Is referral of a case of work from one human resource to another one depending on their social relations? In fact, what fraction of human resources' commercial interactions have been formed based on the relation between two human resources who are connected in the social network SN' _L ? We studied it for different flows in event logs. The value of the link dependency adds to set X as one of the values.

Behavioural Conformance Checker (SF3)

To answer the second question of the research, we suggest SF3. In fact, with the assumption of the effect of social relations on the formation of interactions between human resources, we anticipate the secondary network of the name 𝐴𝑁_𝐿′ based on triadic closures. The relations of network 𝐴𝑁_𝐿′ are based on this human resources' behaviour that they refer jobs to their social friends. Then we calculate the conformance rate of the real activity network 𝐴𝑁_𝐿 with the 𝐴𝑁_𝐿′ which is formed based on the social network SN' _L . The similarity of these two networks is reported as the behavioural conformance rate between networks 𝐴𝑁_𝐿 and SN' _L . (because network SN' _L influenced the formation of network 𝐴𝑁_𝐿′ relations). Then, by evaluating and statistical analysis of the results, we prove that the assumption of the influence of social relations on the formation of the interactions among human resources is correct. In addition, network 𝐴𝑁_𝐿′ has not been created in terms of chance and luck, and network SN' _L relations have affected them. Since the network 𝐴𝑁_𝐿′ is formed on the basis of work referral behaviour which is based on the research hypothesis, this step of the study is called behavioural conformance checker.

A salient point in the triadic closure mechanism's generalization is that the triadic closure has been introduced in the context of one (social) network [40], [93], [101], but we expand it to the context of two different networks. If social relations influence the collaborations among the individuals in the business process, then, considering the generalization of the triadic closure mechanism, the expected activity network AN' _L is defined for each layer (each flow) based on definition 5. The extraction of network AN' _L is carried out by P05 in figure 4.

Definition 5: AN' _L = (𝑉 _{𝐴𝑁’𝐿} , 𝐸 _{𝐴𝑁’𝐿} ) is defined as a static and undirected activity network. 𝑉_{𝐴𝑁’𝐿} is a set of human resources, and we have 𝑉_{𝐴𝑁’𝐿=} V _AN . E _an’L ⊆𝑉_{𝐴𝑁’𝐿 ×} 𝑉_{𝐴𝑁’𝐿} which is a set of predicted relations based on the social network of human resources. Two conditions for linking two individuals in the network 𝐴𝑁_𝐿′ are determined. The proposed mechanism is performed by the function Add_Edge_Predictably_Triadic_Closure in algorithm 1.

Condition 1: There are three individuals 𝑟_𝑖, 𝑟_𝑗, 𝑟_𝑘 in a social network, based on figure 5 (a). There is also, two social relations 𝑟_𝑖𝑟_𝑗 and 𝑟_𝑖𝑟_𝑘 between them and no more information about the network are available.

Human resource 𝑟_𝑖 has accomplished his task due to his role, and in the next step, he refers the case of work to the resource 𝑟_𝑖 𝑟_𝑗 or 𝑟_𝑘 with the probability of 𝑝 (the value of 𝑝 is based on the link dependency). Resource 𝑟_𝑗 and 𝑟_𝑘 are friends of 𝑟_𝑖 according to the social network structure. Since the authorized activities range of human resource 𝑟_𝑖 due to his role is limited and specified, his referenced works are also limited, specified and similar. If the resource 𝑟_𝑖 refer some works to resources 𝑟_𝑗 and 𝑟_𝑘, thus, the resources 𝑟_𝑗 and 𝑟_𝑘 will carry out joint activities (regarding the joint activity scenario) while they will be linked to each other in the activity network with the probability of 𝑝² (equation 1). The relationship between the two resources 𝑟_𝑗 and 𝑟_𝑘 in the expected activity network is drawn by a dashed line in figure 5 (a). Thereupon, it is expected that these two nodes will also be in one community. The resources 𝑟_𝑗 and 𝑟_𝑘 could be the ordinary or popular individuals in social network SN' _L .

(2)

Condition 2: In accordance with figure 5 (b), there are five individuals of 𝑟_𝑖, 𝑟_𝑗, 𝑟_𝑘, 𝑟_𝑙 and 𝑟_𝑚 and four edges of 𝑟_𝑖𝑟_𝑘, 𝑟_𝑖𝑟_𝑘, 𝑟_𝑙𝑟_𝑗 and 𝑟_𝑘𝑟_𝑚 in the social network.

Resources 𝑟_𝑙 and 𝑟_𝑚 are linked to each other if the resources 𝑟_𝑗 and 𝑟_𝑘 are connected based on the condition 1, and according to the condition 1, the edges 𝑟_𝑙𝑟_𝑗 and 𝑟_𝑘𝑟_𝑚 are not formed. If edges 𝑟_𝑙𝑟_𝑗 and 𝑟_𝑘𝑟_𝑚 are predicted and the edge 𝑟_𝑙𝑟_𝑚 is added based on the condition 2, it means that four individuals ??_𝑗, 𝑟_𝑘, 𝑟_𝑙 and 𝑟_𝑚 have performed joint activities and have the identical role. Hence, referring work from the resource 𝑟 𝑗 to the resource 𝑟_𝑙 or from the resource 𝑟_𝑘 to the resource 𝑟_𝑚 is not possible. The probability of referring work from the resource 𝑟_𝑖 to the resources 𝑟_𝑗 and 𝑟_𝑘, also from the resource 𝑟_𝑘 to the resource 𝑟_𝑚 and from the resource 𝑟_𝑗 to 𝑟_𝑙 is equal to 𝑝. Consequently, the probability of establishing a relation in the network AN' _L between the resources 𝑟_𝑙 and 𝑟_𝑚 regarding their independence from each other is 𝑝⁴ (equation 2). Similar to the condition 1, the resource 𝑟_𝑙 and 𝑟_𝑚 could be the ordinary or popular individuals in social network 𝑆𝑁_’𝐿

(3)

The condition 2 can expand; in fact, the referral of work can be cascaded down to other human resources through their social relations. This referral expansion was ignored since the probability for building a relationship in the network AN _'L has dropped significantly.

Since the number of the predicted edges may be less than the number of network 𝐴𝑁_𝐿 edges and the comparison becomes impossible, thus, the difference between the number of 𝐴𝑁_𝐿 and AN' _L edges is provided through a random method using the function Add_Edge_Randomly.

After constructing the network AN' _L , the study of conformity and structural comparison are conducted between two networks 𝐴𝑁_𝐿 and AN' _L for different layers. Regarding that structural comparison of two networks 𝐴𝑁_𝐿 and AN' _L is considered and two sets 𝑉_{𝐴𝑁’𝐿} and 𝑉_𝐴𝑁𝐿 are equal together. Therefore two sets 𝐸_{𝐴𝑁’𝐿} and 𝐸_𝐴𝑁𝐿 must be compared with each other. This operation accomplishes by the P06 in figure 1 and the function Calculate_Conf_Rate in algorithm 1. The metrics used to measure the conformity or similarity of these two sets are Jaccard and Sørensen-Dice coefficient.

The Jaccard index, also known as the Jaccard similarity coefficient, is a statistic to compare the similarity and diversity of sample sets. The Jaccard coefficient measures the similarity among finite sample sets (for example X and Y), and it is defined by the size of the intersection's sample sets divided by the size of the union of the sample sets (equation3). This metric is in the interval [0, 1] [42], [78].

(4)

The Sorensen-Dice index is a statistic for comparing the similarity of two sample sets. It was developed independently by the botanists Thorvald Sorensen [76] and Lee R. Dice [26], published in 1948 and 1945, respectively. Sorensen-Dice is called F1-score and Dice similarity coefficient (DSC). DSC is calculated based on the Equation 4. The DSC is a relative similarity in the range of [0, 1].

(5)

The value of similarity between networks 𝐴𝑁_𝐿 and AN' _L is one value of the set 𝑋. Therefore, 𝑋 is a set of values which determines the conformity status for two networks. SF03 in figure 4 is implemented through Python and networkX library.

5.2 Evaluation Strategy

Conformance checking is conducted by comparison of primary default models with extracted models from real event logs. Since in structural conformance checking (SF02) the comparison is based on the value of predefined metrics and concepts of social network analysis, the evaluation is not necessary. But of course, behavioural conformance checking requires evaluation step. Although we have predicted the expected activity network AN' _L ) based on the social network, our problem is not network prediction. Thus, the evaluation of our model is not performed by dividing the dataset into two sets train and test.

The network AN' _L is formed with the hypothesis of the effectiveness of social relations on the formation of business interactions, along with we compare the real network 𝐴𝑁_𝐿 to AN' _L . Consequently, it should be ensured about the results. Thus, the Friedman test is applied to validate the results. We use this test to compare the results when activity network is built full randomly (CCRL) and when created based on the network 𝑆𝑁 (CCTC) to determine that formation of relations in the activity network is influenced by social relationships structure. The random activity network is called 𝐴𝑁^” _𝐿. This network is constructed according to algorithm 2 and its conformity with real activity network 𝐴𝑁_𝐿 is investigated.

Definition 6: is defined as a static and undirected network. 𝑉_𝐴𝑁𝐿 ^" is a set of human resources, and we have . which is a set of random relations among the human resources based on the Erdos-Renyi model [62].

Given that our modeling is based on multi-layered networks, for more accurate evaluation, the results of structural and behavioural conformance checking will be presented for modeling activity network based on the simple network too. Therefore, we consider the simple activity network as follows.

Definition 7: according to the definition of simple networks [99], 𝐴𝑁_𝑆 = (𝑉_??𝑁𝑆’,𝐸_𝐴𝑁𝑆) is defined as an activity network (or workflow network) which is one-layered, static, undirected, and weighted. 𝑉_𝐴𝑁𝑆 is a set of human resources and we have 𝑉_𝐴𝑁𝑆 ⊂ 𝑉_𝑆𝑁, in other words, 𝑉_𝑆𝑁∩𝑅 = 𝑉_𝐴𝑁𝑆 and 𝑉_𝑆𝑁∩𝑉_𝐴𝑁𝑆 ≠ 𝜙. 𝐸_𝐴𝑁𝑆 ⊆ 𝑉_𝐴𝑁𝑆 × 𝑉_𝐴𝑁𝑆. is a set of relations based on joint activities between human resources. For example, there is an edge between the two vertices 𝑖 and 𝑗 when 𝑖 and 𝑗 have at least one same activity, such as 𝐴_𝑛, in the various executions of business processes. Therefore, in this network, unlike the network 𝐴𝑁_𝐿, the type of flow exchanged between human resources does not matter. The number of joint activities between 𝑖 and 𝑗 is defined as the weight of their relation.

Similarly, the social network corresponding to human resources in 𝐴𝑁_𝑆 will also be defined as definition 8.

Definition 8: given the previous definitions, 𝑆_𝑁𝑆′ = (𝑉_𝑆𝑁 ^’ _𝑆 ^′, 𝐸_𝑆𝑁 ^’ _𝑆) is defined as a static, undirected and unweighted social network so that 𝑆𝑁^’ _𝑆 is a sub-graph of 𝑆𝑁. 𝑉_𝑆𝑁 ^’ _s ⊂ 𝑉_𝑆𝑁 is a set of individuals that includes individuals in the network 𝐴𝑁 𝑆 and their friends. Similarly, 𝐸_𝑆𝑁 ^’ _𝑆 ⊆ 𝑉_𝑆𝑁 ^’ _𝑆 × 𝑉_𝑆𝑁 ^’ _𝑆 is a set of friendship relationships between individuals.

All the notations employed in the research with their descriptions are listed in table 2.

Table 2: Research notations and description 

6.1 Dataset

Our research dataset is simulated based on user behaviour modeling of an Iranian ECSE called Digikala during the period October 1, 2016, to 20 November 20, 2016. Business processes and user behaviour are modeled and simulated by the WoPeD tool with regard to real data of the Digikala. Generating a dataset by simulating based on actual behaviours and patterns has two advantages in comparison with real dataset: 1) The actual data includes a set of specific behaviours in the data collection time period. Consequently, not all possible behaviours are included or some behaviours are very low-frequent. So by changing the simulation settings, you can create more behaviours and examine them, and 2) When the dataset is limited to reality, the results are limited to the same specific case study. Even the size of the dataset can have a small volume. Hence the results cannot be reliable and the answers will not be decisive. But when the dataset is obtained by simulation based on modeling the user behaviour, it includes different possible cases and can be generated sufficiently; thus, the results will be more reliable and more certain. In many other studies [13], [30], [54], [55], [56], [59], [60], [71], user behaviour modeling and simulation techniques have been used to provide an appropriate dataset when there is no sufficiently adequate dataset.

The dataset includes two parts: 1) DS01, the dataset of the social network SN. The characteristics of DS01 are given in Table 3, and 2) DS02, the dataset of the event logs 𝐸𝑣𝑒𝑛𝑡𝐿𝑜𝑔 that its features have expressed in definition 2.

Table 3: Characteristics of dataset DS01 (network ) 

To ensure the experimental results, the dataset DS02 has two samples (DS02-s1, DS02-s2). Each sample includes four versions. Each version consists of the execution of 1000 various instances (or cases) of some electronic purchasing processes. The process involves the structure of the loop. The number of different main procedures is over 16. The number of event logs' records in DS02-s1 and DS02-s2 is 6216 and 6115, respectively.

The activity network 𝐴𝑁_𝐿 based on the joint activities and various flows can be extracted for each version of DS02. For each activity network 𝐴𝑁_𝐿, a corresponding social network 𝑆𝑁_𝐿′ can be selected from the social network 𝑆𝑁. The naming of the networks is as follows; for instance, S1-ANi-v1 and S2-SNg'-v2. The first one is based on the information interactions, and it is extracted from the first version of the first sample. The second name belongs to the social network of the people who are involved in the second version processes of the second sample and are related to the goods interactions. Furthermore, S1-ANs-v1 is the extracted activity network from the first version of the first sample which includes all the flows.

6.2 Results of Structural Conformance Checking

Since we are interested in checking the structural conformity between two networks 𝑆𝑁_𝐿′ and 𝐴𝑁_𝐿, we examine and compare these two networks from different aspects: structural features of the network, homophily, social role (popularity) and link dependency. The results are the answer to the research questions, especially Q1.

6.2.2 Homophily

In the activity networks, people are divided into two main groups: 1) the people who are human resources in the commercial processes, and 2) the people as customers who carry out some tasks through social commerce systems in the commercial processes. To check the link homophily, we examine two situations: 1) based on all the people in the activity network and social network and 2) based on the people are only human resources. Figures 12 to 14 and figures 15 to 17 respectively indicate the results.

Figures 12 to 14 (a) and figures 15 to 17 (a) indicate the probability of establishing a relation between two vertices in the activity network based on the number of their mutual friends in the social network. Figures 12 to 14 (b) and figures 15 to 17 (b) demonstrate the change of the probability of the forming a relationship between two nodes based on the number of mutual friends in the social networks and relative to the previous state in the chart. For instance, in figures 12 to 14, (a) AN _i , the linear charts for various versions of the dataset have overlap and low differences. In general, with the increase in the number of common neighbors between two individuals in network 𝑆𝑁_𝐿′, the connection probability of these two individuals will increases, although the growth is at a low rate. Changes of connection probability are disclosed clearly in figures 12 to 14, (b) AN _i .

When people are only human resources, the results are different. For example, figures 15 to 17, (a) AN _i indicates the probability of building relationships among human resources does not have a regular trend with the increase in the number of mutual neighbors. For the value set of {2, 3, 4}, the probability of linking is relatively more than the other values in figures 15 to 17, (a) AN _i . Although the likelihood of developing a relationship for 9 common neighbors is high, the number of connections for this value is very small (e.g., the highest number is 2, which is 2/6 = 0.33). Changes of connection probability in the activity networks based on the information flow are presented in figures 12 to 14, (b) AN _i for the number of common friends.

Table 4: Structural characteristics of different activity networks and corresponded social networks 

Figure 6: Graph and degree distribution chart of social network S1-SNi'-v1 

Figure 7: Graph and degree distribution chart of activity network S1-ANi-v1 

Figure 8: Graph and degree distribution chart of social network S1-SNg'-v1 

Figure 9: Graph and degree distribution chart of activity network S1-ANg-v1 

Figure 10: Graph and degree distribution chart of social network S1-SN'S-v1 

Figure 11: Graph and degree distribution chart of activity network S1-ANS-v1 

6.2.4 Link Dependency

Is referring a case of work from one human resource to another one depending on their social relations? We studied it for different flows in event logs, and the results have been reported in table 5. Various versions of the dataset have different social link dependency. Version 4 (S1-v4 and S2-v4) has the most link dependency. Hence, it is interpreted that with the probability of 𝑝, human resource 𝑟_𝑖 refers work to human resource 𝑟_𝑗 if 𝑟_𝑖 and 𝑟_𝑗 are connected in the social network. The value of 𝑝 for the version S1-v3 based on the information flows is equivalent to 0.42.

Figure 12: Homophily of link for all the people in the activity network AN_i based on the corresponded social network 

Figure 13: Homophily of link for all the people in the activity network ANg based on the corresponded social network 

Figure 14: Homophily of link for all the people in the activity network ANS based on the corresponded social network 

Figure 15: Homophily of link for all HRs in the activity network ANi based on the corresponded social network 

Figure 16: Homophily of link for all HRs in the activity network ANg based on the corresponded social network 

Figure 17: Homophily of link for all HRs in the activity network ANS based on the corresponded social network 

Figure 18: Popularity status of connected people in activity networks, relative to the corresponded social networks 

Figure 19: (a) Popularity status of connected HRs in the activity networks, relative to the corresponded social networks (b) Popularity frequency of connected HRs in the activity networks 

Table 5: Link dependencies based on different flows for different versions of the dataset 

6.3 Results of Behavioural Conformance Checking

Algorithms 1 and 2 are dependent on the stochastic theory. Hence, the results of each implementation of these algorithms may not be the same. Thus, the behavioural conformance checking results for an average of 1000 different implementations on the datasets S1 and S2 are reported in table 7. Algorithm 1 has two extensions, that is, CCTC1, and CCTC2. The edges between two popular nodes are ignored in CCTC1, while in CCTC2, they are not removed.

Regarding table 7, the conformance rate for network 𝐴𝑁_𝐿 (𝐿={ 𝑖,𝑔})with network 𝐴𝑁_𝐿’ is in most cases more than the conformity of network 𝐴𝑁_𝐿 with network 𝐴𝑁_𝐿". Thus, it is concluded the relations in the activity network are affected by the social network's structure. Moreover, the conformance rate based on the CCTC2 is greater than the CCTC1 for the layers of goods and information. Especially, the value of the similarity index is greatest for CCTC2 in all cases at network 𝐴𝑁_𝑔. It is justified by structural conformance checking results in section 5.1.

Table 6: The set X based on the structural conformance checker values for human resources 

Owing to the results of structural conformance checking, it was predictable that the actual behaviour of human resources would be hidden if the different flows as the network layers were not separated from each other. Hence, the CCTC1 and CCTC2 algorithms did not obtain better conformance rate in comparison with CCRL when the activity network is modeled based on the simple network. Thus, multi-layered network modeling in the context of s-commerce systems is more accurate and suitable for mining the comercial processes and organizations. Every row of each comparison in table 7 is equivalent one value of set X. It is represented that CCTC2 has the best values.

Evaluation of Behavioural Conformance Checking

The Friedman test is a non-parametric statistical hypothesis test. It is applied to investigate whether there is a meaningful statistical difference among the results, and to compare and validate the performance of algorithms [65]. Due to stochastic and random characteristics of CCTC1, CCTC2, and CCRL algorithms, this statistical test is required. Therefore, this test is performed between the CCTC algorithms and the other one (CCRL). The null hypothesis in the Friedman test (H₀) states the equality of medians among algorithms, whereas the alternative hypothesis (H₁) shows the difference. Significance level (a) illustrates the probability of the null hypothesis rejection while it is true. If P-value were less than the significance level, H₀ would be rejected. Further details on nonparametric statistical tests are found in the study of Derrac [25].

Calculation of ranking is the first step in the Friedman test. Average ranking is applied to rank each algorithm, and equal values are given to the average ranks [65]. Table 8 shows the ranks for each of the employed algorithms. Due to the ranks for both Jaccard and DSC indexes are equal, we reported both of them in one table. As can be observed, the algorithm CCTC2 has provided the first rank for the activity networks based on the information and goods flows. Besides, algorithm CCTC1 has obtained the second rank for information flow based activity network. The algorithm CCRL has the first rank in the activity network based on the simple network modeling. In other words, when there is no distinction among flows, CCRL has gained the better rank.

The P-value and Chi-square values of Friedman's test are listed in table 9. From the Chi-square distribution table, the critical value for (3-1)=2 degree of freedom with a 0.05 significance level is 5.99. Regarding table 9, Chi-square values for all datasets and activity networks are higher than the critical value. It means that H₀ is rejected while H₁ is accepted in all cases. Furthermore, the P-value is very small for all experiments, which affirms the rejection of H₀. It demonstrates a significant difference in the behaviour of the algorithms. Table 9 confirms that there is a statistically significant difference among the algorithms CCTC1, CCTC2, and CCRL. Moreover, our proposed algorithm results are not obtained by chance, since the gained P-value is less than 0.05 in all cases, except for versions s2-v1 for the networks 𝐴𝑁_𝑖. Due to the probability value is very low (𝑝=0.04 in version S2-v1 for 𝐴𝑁_𝑖, the Friedman test is rejected. Whereas the probability of linking two nodes per equation 1 is 0.0016, which is very low. Therefore, our study hypothesis is proved.

Table 7: Similarity for an average of 1000 implementations 

Table 10 displays the cases in which the CCTC2 is better, worse, or equal to other algorithms. The algorithm CCTC2 is performed better than other ones in most of the cases, except for network 𝐴𝑁_𝑆. Since there is no difference among flows in network 𝐴𝑁_𝑆, the reality of human resources' behaviour could not be observed. Therefore, it infers that the CCTC2 has not gained better performance for the activity networks which is modeled based on the simple network.

Table 8: Friedman's ranking based on the Jaccard and DSC indexes for algorithms CCTC and CCRL 

Table 9: Friedman's test results for different versions of datasets and activity networks 

Table 10: Pairwise comparison between algorithm CCTC2 and other algorithms 

8.1 Implications

The conformance checking compares the real execution of a business process with the original process model [16], [79], [92]. In fact, in the process model discovery approach, the process model discovered from the event log is compared with the initial model. A process model is a network of tasks with logical relations. In this research, we examined the conformance checking in the organizational mining approach. The initial model is the structure of the relations among individuals (i.e., human resources). The structure of the individuals' links can be official or unofficial. An official structure is one of a variety of organizational structures; while unofficial structures are based on social relationships, email, telephone calls, and so on. A network structure can extract from every official/unofficial structure among human resources through a well-defined scenario. Similarly, the model discovered from the event logs in the organizational mining approach can be the organizational structure extracted from the event logs. It can also be the activity networks extracted from the event logs. Therefore, in organizational mining, the networks contain human resource relations. In this study, the conformance checking of the social relations’ network with the activity network of human resources was considered.

In recent years, due to the expansion of social networking applications, especially in a variety of businesses (e.g., social commerce), the study of social networks and activity networks is becoming increasingly important simultaneously. Due to the diverse flows in the social commerce systems and IoT-based systems in the future, the proposed framework can be of considerable use for studying users (i.e., human resources) behaviour. It is worth noting that the type of each exchanged flow among business resources should be specified and recorded in event logs. The type of exchanged flow among resources as contextual and semantic information is essential.

Among the important applications of the proposed framework are evaluating the performance of the organizational resources and identifying the individuals effective in the formation of business relationships and cooperation among individuals. Hereupon, studying the effect of unofficial relationships on the development of business relationships and the identification of the productive structure on the execution of a process rather than a formal or predefined structure are some of the applications of the proposed framework. Consequently owing to the influence of social relations on business interactions, the prediction and management of business markets are possible. It conveys a significant implication for business process managers, researchers, and practitioners interested in social commerce.

This study presents several managerial implications. First, the findings show that not only social relations affected on the customer behaviour, but also affected on the formation of the cooperation among human business resources. Therefore, improvement of social relations among human resources can influence the business process performance. Second, discovering the social structure that affects the activity network of the human resources can affect human resource management and business profitability. At last, according to the recent research by Chang [18] and Chau [19], the identification of individuals and social relations that influence the business process can facilitate and accelerate the prevention and detection of fraud and smuggling.

8.2 Future Works

Applying network modeling, in particular, multi-layered networks and employing social network analysis methods, especially the link prediction, exposes a novel research direction in conformance checking and organizational mining. There are many potential future research directions for this work. First, if the human resources can play several roles in the process, then what features will have the activity network based on the joint activities? Second, if the activity network is extracted based on the handover of work scenario, then a directed network will be created. How will the conformance checking of the directed activity network be carried out with the undirected social network? Third, how do other social relations (e.g., messaging network, e-mail network, call network, etc.) form the business interactions (i.e., activity network)? Which one has more effect on the activity network? Finally, theorizing on why and how people build business interactions with each other based on social relationships in different kinds of commercial social networks is an intriguing direction for further research. Can the activity network be constructed from social relations? Furthermore, although there was no proper dataset during the research time, we intend to investigate real dataset to gain more trusted evaluations in the future. Eventually, we hope that the findings of this research can help researchers to identify new research questions and may open the door for future research.