^{1}

^{*}

^{2}

Reviewing the existing literature is the preliminary stage of any research work. In the recent times, researchers have enormous sources to gather literature data related to their research topics, particularly from online journals, directories, and databases. The online sources such as Scopus, Google Scholar, and Web of Science facilitate the researchers to know the updates and current state of the research domains. In traditional methods, a researcher had to collect the related research works, review them, code the information and present them in a narrative manner to specify the research gap in the existing studies. Presentation of a review of earlier studies is not a mere summary of description of earlier studies; it provides critical arguments on hypotheses to be considered and suitable methodology to investigate the topic, list of variables to be investigated, and so on. However, if one considers a huge volume of earlier studies, consolidating the information available in them is not an easy task. Critically exploring the hidden information and patterns in the existing studies, developing a visual/graphical representation of information from the data, and summarizing information through suitable metrics are gray areas in reviewing the existing studies. To overcome these issues, the study attempts to use principles from Graph Theory and proposes a new methodological approach to do the review of literature. Domains such as Sociology and Psychology have recognized the usefulness of Graph Theory, a branch of Mathematics and applied the principles to social network analysis (SNA). SNA adapts metrics such as degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, cluster analysis, and modularity to identify the influential actors (nodes)/persons in the social networks. In this paper, these SNA metrics are compared with analyzing literature data to identify the influential variables in the literature, relationships among variables, and strength of relationships to develop suitable research problems, prioritizing the research problem, identification of variables for the study and to develop hypotheses. The sample literature articles are organized in a structured data and the structured data are visualized through a network graph. Furthermore, the network graph is analyzed by graph visualization and manipulation tools such as Gephi, UCINET, Graphviz, and NodeXL. Gephi 0.9 is used for network graph analysis and the graph theory metrics are investigated for the collected literature data.

Reviewing earlier studies is a starting point of many research problems. An efficient reviewing process provides a foundation for advanced knowledge and theory development; also it shows the fit of research areas in the existing body of knowledge and uncovered area where research is required [

SLR is naturally an iterative process, supported by defining proper keywords for search, identifying the relevant literature, analyzing screened literature, and structuring the literature data for further analysis. Literature analysis is carried out in different ways. Development of various graphical visualization and manipulation tools is facilitated for literature review; to name two: bibliometric analysis is performed to find author affiliation and keyword statistics and network analysis to identify the relationship between the citation analysis and topical content. These procedures are helpful in developing an abstract research problem; however, these procedures fail to recognize patterns, insights into variables, and volume of support for existing dimensions. To overcome these issues, a network representation of existing literature is constructed and the principles from Graph Theory are applied to draw inferences to the literature pool. A network is a connection between two or more entities. The entities may be anything, viz., human beings, machines, animals, buildings, characters in a movie, keywords, objectives and variables in literature, and so on. In Graph Theory topology, these entities are considered as nodes (vertices) and the relationship between these entities is portrayed by edges (ties) connecting these nodes [

A directed graph is one in which the nodes are connected with a direction (arrow head); in simple communication terminology, there is a sender node and a receiving node; the graph is strongly connected if there is any direct relationship/path from any nodes to any other nodes. The directed graph portrays the relationships such as friendship network, family network, and transportation network. The undirected graph is connected to the nodes in the network without any direction from any nodes to any other nodes [

The graph in

Now let us consider n as the number of nodes and e as the number of edges. The graph represented in ^{1} is connected to three different nodes n^{2}, n^{3}, and n^{4} with three different relationships (edges) and e^{1}, e^{2}, and e^{3} without any arrowhead direction. This network may be a friendship network, family network, coauthor network, literature variables network, and so on. By seeing the network, one can guess that node n^{1} is the most connected and it might be an influential node in the network; influential, in the sense that it has three different relationships with other nodes in the network. Consider this network as a case of

friendship network; then, extending the principle of connectedness in the graph theory, one may consider node n^{1} as the influential person in the network than others, since others have only one connection.

Let us consider the same network in a literature review context; assume, “n” as number of variables in the research papers pool (n = 4), and “e” as the relationships between any pair of variables (e = 3) in the research papers. Now we can say that the variable n^{1} is related to three other variables in the collected literature pool (three connections/relationships); the other variables n^{2}, n^{3}, and n^{4} are studied once with n^{1} (one connection/relationship); from this analysis, comparatively, the variable n^{1} is the highly connected and most active/popular variable in the literature collection.

Thus, by comparing the relationship among the variables in the literature collection with a Graph, one can relate various metrics in the Graph Theory to analyze literature networks. The metrics such as degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, cluster analysis, and modularity, which are descriptive measures for a graph, are adopted for deep mining of the literature data in this paper. To build the arguments on the proposed methodology, researchers compare two sample cases: one, a Facebook friendship network and another one, a literature variable network.

The research work is organized as follows: a briefing of the purpose of the proposed research work; then, a section to present a model of graph theory metrics such as degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, cluster, and modularity for analyzing the literature variable network; further a section devoted to the applicability of proposed methodology based on a case explanation, followed by elaborating the results and discussions of the proposed metrics. Also, limitations of the study, direction for the future research, and concluding comments are placed at the end of this paper.

In the past, researchers faced several limitations and constraints; accessing the research work were limited and very few online repositories published periodical updates on researches. Open sources repositories and abstract index services were also limited in number and few niche research communities such as consulting firms, research laboratories, and government agencies know the progress and updates of research problems. Rapid growth in Information and Communication Technologies (ICT) paved way to the availability of a large number of electronic resources, repositories and open source journals, directories, and indexing services and facilitate the research communities across continents.

If a researcher needs literature data of a specific topic, the keyword of the specific research topic is selected and searched in online databases such as Google scholar and Scopus. The results obtained from the online databases are vast (more than a thousand for a selected research topic) and to read and analyze each and every document is not humanly possible. So selecting the limited number of research work, which are centrally positioned in the research topic, rather than collecting enormous number of research [

Filtering is a process of restricting less-proximate topics; for example, filtering the literature data based on certain periods of time, top-tier journals, or any single journal, which is pioneer in that particular research field. By this process, he/she narrows down the domain for keyword search; and research work meeting out such search criteria will be often countable in number. For a hypothetical case, let us consider a situation where the count is around 250 articles. In the next step, the researcher will read and gather the information of each and every 250 articles. The information may be classified into geographical data and article content data as shown in

The geographical data give complete details of the authors, year of publication, publisher details, citations, authors and co-authors, and so on. These data show the geographical flow of particular research in various domains, such as environment and communities. Article content data provide details in the internal aspect of the article. Internal aspects elaborate the particular problem addressed in the article, the theories followed and proposed, fixation of hypothesis, selecting the dependent and independent variables, methodologies adapted address the problem, techniques and metrics used for analysis and interpretations, and so on. These are the internal data collected from the literature, by reviewing them. Now consider the data classified on the basis of

All the authors, of 250 articles, have researched the same topic, related issues, and problems. Each and every author has researched the topic based on different

S. No. | Geographical data | Article content data |
---|---|---|

1 | Author Name | Title of the Article |

2 | Co-author Name | Abstract |

3 | Authors Country | Keywords |

4 | Author Affiliations | Objective |

5 | Journal Name | Theories |

6 | Journal Volume Number | Hypothesis |

7 | Journal Issue Number | Variables and Dimensions |

8 | Article Page number | Methodology |

9 | Article Citation Number | Scope and Purpose |

10 | Digital Object Identifier (DOI) | Identifications |

11 | Journal Publisher Details | Improvements |

12 | International Standard Serial Number (ISSN) | Conclusions |

13 | International Standard Book Number (ISBN) | Cross-References |

types of objectives, hypotheses, theories, variables, and methodologies. The results obtained by the researchers too differ from one work to another. But the critical task for a researcher is to gain significant insight into research variables, relationships measured, status of hypotheses tested, and important/influential variables/hypotheses to be considered for further research.

For example, a researcher structures the information from 250 articles as shown in ^{th} article, he noticed that attitude towards advertisement, brand loyalty, and purchase intention are addressed; but

Paper No. | Year | Authors | Journal name | Title of the article | Purpose | Theories | Variables | Methodology | Results |
---|---|---|---|---|---|---|---|---|---|

1 | |||||||||

2 | |||||||||

3 | |||||||||

4 | 2012 | Choi and Rifon | Psychology and Marketing | It Is a Match: The Impact of Congruence between Celebrity Image and Consumer Ideal Self on Endorsement Effectiveness | Celebrity Consumer Congruence, Celebrity Product Congruence, Attitude toward advertisement, Attitude toward the brand, Purchase Intention | ||||

-- | |||||||||

-- | |||||||||

-- | |||||||||

60 | Attitude toward advertisement, Brand Loyalty, Purchase Intention | ||||||||

-- | |||||||||

127 | |||||||||

-- | |||||||||

-- | |||||||||

250 |

these variables may be a partial set of variables used by another researcher, say in the 4^{th} article. Thus, these two articles may be considered to be similar, based on the same set of variables considered; article number 127 could have used only purchase intention and brand loyalty. Thus, article 127 is partially closer to 60^{th} and 4^{th} articles. So, many relationships might exist in the large number of literature collection, remembering all this information is a tedious task for any researcher. This type of similarity identification manually is not possible for all the 250 articles. Hence, by identifying similarities among the existing research work, a researcher may define a set of highly influencing variables, another set, which is less influential, and a set of variables acting as intermediate (moderators/mediators).

Hence, there is a need to develop a conceptual framework and related metrics to review voluminous literature data, detect various relationships, and rank them in the order of frequently studied by the researchers. Such identification will help the research community to know the advancement and progress related to a research topic. To analyze the literature articles and to identify the variable-based influential (similar) information of selected topics, the paper introduces a social network analysis (SNA) metrics and also elaborates how to construct a structured literature variable data for analyzing through Gephi 0.9, open source SNA software.

Freeman (1978) was the first to draw a graph called star graph (

This person/node has the highest degree of relationship (edge) between all others persons/nodes and it falls between all other nodes; also, it has the shortest path lengths when compared to all other nodes and is also viewed as a closest person/node in the network. These notions of centrality, viz., degree, betweenness, and closeness, are translated into unique measures of centrality and are explored in the following subsections.

Many of us already know, intuitively, the meaning of centrality in an SNA; it is the central position of a network/graph, represented through a person/node, which tends to be more visible in the network [

give a rough indication of the social power of a person/node based on how well they are connected in the network [

Degree centrality generally considers the number of connections or number of immediate contacts a node has in a network. To measure degree centrality, add the total number of edges/relationships connected to a node with other nodes in the network. For now, let us reserve the discussions on the direction of arrows connecting these nodes. Since directions of edges are not considered, it measures the level of activeness of a specific node in the network but does not show the power/influence/popularity of the node in the network.

The equation to calculate the degree centrality of any node “i” is given below:

C d ( i ) = ∑ j = 1 n x i j = ∑ i = 1 n x j i

C_{d} = degree centrality;

x_{ij} = the value of the edge from node i to node j (the value may be either 0 or 1);

x_{ji} = the value of the edge from node j to node i (the value may be either 0 or 1);

n = the number of nodes in the network.

Degree centrality does not look at the direction of edges and this centrality is useful for analyzing symmetric data, i.e., only simple graph not for di-graphs (directed graph). For a directed graph, the degree centrality is classified into two types: In-degree and Out-degree centrality. In-degree centrality is the count of edges received by a node from others, and out-degree centrality counts the edges that emanate from a node to others. The popularity of the node is identified by in-degree centrality and out-degree measures the expansiveness of the node. The equations to compute in-degree and out-degree are given below:

In-degree out-degree

C i ( i ) = ∑ j = 1 n X j i , C o ( i ) = ∑ j = 1 n X i j

X_{ij} = the value of the edge from node i to node j (the value may be either 0 or 1);

X_{ji} = the value of the edge from node j to node i (the value may be either 0 or 1);

n = the number of nodes in the network.

The degree, in-degree, and out-degree centrality measures are easy to measure and simple to understand. However, these measures are not very powerful, as they do not consider the rest of the network (overall intricacies in the network) and consider only the adjacency relations of nodes.

To measure the centrality position for a node (person) in the network, we need to calculate the betweenness centrality. Betweenness centrality considers the rest of the network when manipulating the score for an individual node. Betweenness centrality captures a different dimension of the centrality; in a social network context, sometimes it is more useful that “how many people you know in a network” rather than “where you are placed in the network”. The idea of placement is whether a node connected is well connected with other nodes in the network.

The calculation is based on how many times the node sits on the geodesic (shortest path) linking two other nodes (actors) together. To calculate the betweenness centrality, the following equation is used:

C b ( k ) = ∑ X i j k / X i j , i ≠ j ≠ k

C_{b} - betweenness centrality;

X_{ijk} = the number of shortest paths linking nodes i and j that pass through node k;

X_{ij} = the number of shortest paths linking node i and j.

Betweenness centrality can be calculated for both directed and undirected graphs.

Closeness centrality considers the entire set of edges in the network while calculating the centrality of an individual node. This measure differs from other centralities measures; degree centrality brings out the active node in the network, betweenness centrality emphasizes potential control over information flow, and the closeness centrality accentuates a node’s independence. The logic of closeness centrality is that if a node is not a central node, the node relies on others to transmit messages through the network [

Thus, in closeness centrality a node is close to many other nodes but still it is an independent node. These nodes can quickly be reached from others without having to rely much on intermediaries. The closeness centrality is not only to measure the independence of the node but also to measure the node’s ability to access information in the network very quickly compared to other nodes [

C c ( i ) = ∑ j = 1 n d i j

where

C_{c} - Closeness centrality;

d_{ij} = the distance connecting node i to node j.

These are the three important centrality measures applied for network analysis to identify the importance of various nodes in the graph.

Eigenvector centrality measures the importance of the link of a node in a network. It assigns relative scores to all nodes in the network based on the principle that connections to nodes having a high score contribute more to the score of the node in question. In simple, the eigenvector identifies the nodes which are not more influential but have a link with a node which is more influential in the network.

Modularity measures the density of links inside communities as compared to links between communities (groups/clusters/communities). The communities will be based on the density of connections between the nodes in the network. At the same time, modularity measures the sparse connections of the nodes between the communities [

Clustering coefficient measures the likelihood that two associates of a node are associates. A higher clustering coefficient indicates a greater “cliquishness” [

These are various SNA metrics applied for network analysis in the current framework. In this paper, these SNA metrics are applied over the literature network to extract the meaningful information from the literature. Furthermore, the next section discusses the applicability of this centrality measures for literature network using a case explanation.

The applicability of the centrality measures for literature review is elaborated through a case example. Consider a case of Facebook friendship network and a literature variable network; both the networks are formatted as digraphs (arrow heads have directions). Friendship network and literature variable network are shown in

The node/person to which ego is directly connected is called as alters in SNA. In this case, consider Rias as an ego and alters are Panneer and Umma. Now let us apply this logic to literature variable network analysis as given in

S. No. | Friends list | Connection |
---|---|---|

1 | PANNEER | VENKAT |

2 | VENKAT | RIAS |

3 | RIAS | PANNEER UMMA |

4 | KASI | PANNEER |

5 | CHITRA | VENKAT |

6 | UMMA | CHITRA |

7 | LAVANYA | PANNEER |

S. No | Research paper | Connection /Hypothesis/Relationships studied | |
---|---|---|---|

Independent variables | Dependent variables | ||

1 | Paper 1 | Celebrity consumer congruence | Attitude towards advertisement; Attitude towards brand; Purchase intention |

2 | Celebrity product congruence | Attitude towards advertisement; Attitude towards brand; Purchase intention | |

3 | Attitude towards advertisement | Attitude towards brand | |

4 | Attitude towards brand | Purchase intention | |

5 | Paper 2 | Attitude towards advertisement | Purchase intention |

6 | Attitude towards advertisement | Brand loyalty | |

7 | Paper 3 | Attitude towards celebrity | Brand loyalty |

8 | Celebrity product congruence | Brand loyalty | |

9 | Attitude towards brand | Brand loyalty |

variables. So extending the concepts of SNA to this literature network, the ego is a node which is directly connected to other nodes (alters); in the literature variable network the independent variables are considered as ego and dependent variables are considered as alters; this may also be vice versa.

In this case, samples of three research papers have been selected to analyze and the papers are based on “Celebrity Endorsement” in a marketing domain. Now consider the independent variable “Celebrity consumer congruence” as an ego and “Attitude towards advertisement” “Attitude towards brand”, and “Purchase intention” as dependent variables studied in the research work, which become alters, as per SNA terminology.

Let us move on from this initial table representation to visual representation; two digraphs are given in

The pin point direction of the arrowhead of the edges represents the node/ person receiving the message from other nodes/persons and fairly opposite if the node sends the message. For instance, select a node PANNEER from

Based on

Now by embedding the metrics applied to draw insight about an SNA to the literature network, a researcher can quickly summarize the information available among the literature/articles collected and importance of each variable and critical relationship which are often studied or rarely studied to identify a research gap.

Degree centrality defines the central position of each node (variable) in a network [

For example, in

In-degree centrality measures the number of relationships (edges) received by an ego node (ego variable) from other alters nodes (alters variable). For example, in

Out-degree centrality measures the number of relationships (edges) given (sent) by an ego node (ego variable) to other alters nodes (alters variable). For example, in

These three measures, viz., degree, in-degree, and out-degree, provides insight to the researchers to understand the positioning of previous research works; significance of a set of variables studied in the past. However these measures do not describe the significant level of other nodes (variables), which are connected to them. Also, these measures do not consider the node’s (variables) influential nature or popularity in literature collection [

Betweenness centrality measures the strength of every node in the network and indicates how often it appears between any two random nodes in the network. The node with higher betweenness score is the more influential in the network, as it acts as a junction for communication between other nodes within the network [

Betweenness centrality differs from degree-centrality in the sense that a node is connected to many other nodes within a cluster (group of nodes) and has few connections to other nodes in other clusters in the network. The node will then be more influential within its cluster provided, it will have less influential connection between other clusters. Thus, Betweenness centrality brings out a node’s interconnections with two or more clusters in the network. In

Betweenness centrality could be useful to throw light on different perspectives of the variables in the literature network; in some cases, the degree centrality of a

node will be high but the Betweenness score of that node may be lower; this indicates that the node (variable) is more active within cluster, but less connected with other nodes in different clusters of same network. Identifying these influential nodes (variables) will give more insights on a research problem. Since the network data for this paper are very small, identification of different clusters is more difficult.

A node’s (variable) independency (ability) in the network is measured by Closeness centrality. It means the selected node is not in the central position (degree) in the network, and it relies on others to communicate messages through the network. Thus, the node is close to many other nodes, but it is an independent node. The node (variable) with high closeness centrality has an ability to easily access information in the network. The closeness of a node is measured by shortest distance path between the nodes (variables) in the network. In

“Brand loyalty” have high Eigenvector score “1”. The adjacent variables to “Purchase intension” are “Attitude towards brand―0.256822”, “Attitude towards advertisement―0.042447”, “Celebrity product congruence―0,” and “Celebrity consumer congruence―0”. For “Brand loyalty”, the adjacent variables are “Attitude towards brand―0.256822”, “Attitude towards advertisement―0.042447”, “Celebrity product congruence―0”, and “Attitude towards celebrity―0”.

The variables, “Attitude towards brand” and “Attitude towards advertisement” has already been proved as influential variables in terms of degree and Betweenness centrality. Thus, if any variable has a close tie (connection) with these influential variables, it can dramatically increase the access of other variables in the network. To identify these variables, the Eigenvector centrality is applied for the literature variable data. The Eigenvector centrality resulted that “Purchase intension” and “Brand loyalty” are important variables connected with influencing variables such as “Attitude towards brand (0.2568)” and “Attitude towards advertisement (0.04244)”.

Modularity measures the strength (dense) of division in network module (clusters/groups/communities). It also measures both the density of the links (edges) inside communities and the links (edges) between communities. The community detection mechanism is usually used to detect the modularity [

At the same time, the variable, “Attitude towards celebrity” has a cluster coefficient value of 0. It shows the importance of the variable in the network as the variable, “Attitude towards celebrity” is not having any other neighborhood variable to form a cluster. The researchers can easily identify these types of unique variables which are not concentrated in literature collection.

A summary of the result of the literature variable network is given in

Variables | Degree | In-degree | Out-degree | Betweenness | Closeness | Eigenvector | Modularity | Clustering |
---|---|---|---|---|---|---|---|---|

Celebrity consumer congruence | 3 | 0 | 3 | 0 | 0.8 | 0 | 0 | 0.5 |

Attitude towards advertisement | 5 | 2 | 3 | 0.5 | 1 | 0.042447912 | 0 | 0.35 |

Attitude towards brand | 5 | 3 | 2 | 0.5 | 1 | 0.256822 | 0 | 0.35 |

Purchase intention | 4 | 4 | 0 | 0 | 0 | 1 | 0 | 0.416667 |

Celebrity product congruence | 4 | 0 | 4 | 0 | 1 | 0 | 0 | 0.416667 |

Brand loyalty | 4 | 4 | 0 | 0 | 0 | 1 | 1 | 0.25 |

Attitude towards celebrity | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |

Modularity is applied for the overall results (

The research work has made an attempt to develop a framework to analyze the literature collection through Graph Theory metrics. The metrics related to Graph Theory are applied to social network analysis to understand the importance of nodes/persons in the network, clusters of people in the network based on communication among them, and connecting two groups of people; in turn, the current research work correlated these metrics to a literature network and demonstrated a methodology to analyze whether the literature collected is related to a specific research problem. These metrics can easily comprehend volume of data to few numbers. A researcher can develop better insights on careful selection of variables, with a view, whether the variables are frequently studied or less frequently studied: a list of variables to be considered as independent and dependent more scientifically based on centrality measures. A set of variables

can also act as intermediary (moderator/mediator) and relate to some distinct topics of interest.

Measures such as modularity develop deeper insights for the researchers to sense how the variables are grouped and studied in the past. This information may be very difficult to cull out from manual/conventional reviews. However, the researchers are expected to organize the literature into some classification table based on their own convenience to develop such metrics. A word of caution on the list of research papers is considered; the method completely depends upon the quality of input matrix given; the software cannot differentiate a good research work from bad one; or a study which is an original work versus a replication work. Thus, a quality of output usability of the metrics is completely a function of the input matrix developed by the researchers.

The proposed research work has a few limitations:

Before executing the proposed methodology, the researchers should develop the structured literature data sets. This will be quite time consuming process and also if the researcher is very new to this particular research topic, it will be more complicated to classify the literature data. It needs expert’s opinion about the topic classification.

If the collected literature data does not has a good number of relationships between the documents, the proposed methodology will not be useful for that particular research topic. In general, the researcher should collect literature articles confining to a list of prior defined key words.

The keyword selection should be more appropriate. If the sets of key words are not related, then it will lead to wrong direction and misinterpretation.

The overall modularity results will not be same for every research. It will be different, according to the metrics results.

This paper examined only a small size literature network data.

The researcher should experiment the proposed methodology with a large size data to obtain most significant information from the selected research topics.

In this paper, “Variables literature network” is considered for examination, but the researcher can also consider other literature data such as Objectives and Hypothesis.

This reviewing methodology is applicable for any type of research work with suitable content classification.

Pachayappan, M. and Venkatesakumar, R. (2018) A Graph Theory Based Systematic Literature Network Analysis. Theoretical Economics Letters, 8, 960-980. https://doi.org/10.4236/tel.2018.85067