Student-course bipartite network
Introduction
As many studies have revealed, if individuals can develop a diverse social network—in which they often interact with acquaintances whose skills and experiences vary widely—they are more likely to thrive in their careers. This possibility is called the weak-tie hypothesis (e.g., Mehreen et al., 2019). For example, these individuals are more likely to be
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exposed to diverse perspectives, enhancing their capacity to solve problems creatively (Baer, 2010)
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exposed to diverse and helpful information, improving their success in a variety of roles, such as science (Fronczak et al., 2022).
Therefore, to enhance the career progress of their students, tertiary education institutions should perhaps help these students develop these diverse networks. They might, for example, organize a range of events, promote communities of practice, or attempt an array of other initiatives.
Yet, as Israel et al. (2020) demonstrate, tertiary education institutions might not need to organize these initiatives. Instead, if these institutions choose and design their courses appropriately, these networks may evolve naturally. To illustrate, some courses or sequences of classes integrate diverse students who would otherwise not meet each other. These courses might enhance the social networks of these students.
Israel et al. (2020) designed a tool, called student-course bipartite networks, to achieve this goal. To illustrate
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this tool can generate a table the resembles the following example
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each row corresponds to a separate course, unit, or sequence of classes
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each column presents a separate metric
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for example, if the degree centrality is high, the course enables many students to meet—because many students, from diverse academic disciplines, enroll in this course
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a low clustering coefficient indicates these students would not have met otherwise—perhaps because they do not know anyone in common
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the final column indicates whether the classes tend to be lectures, laboratories, remote but live, or recorded tutorials. If students meet in small but live tutorials, perhaps these relationships are likely to be more productive.
Course | Number of enrolled students | Degree centrality | lLocal clustering coefficient | Format |
|---|---|---|---|---|
Statistics 101 | 20,300 | 0.243 | 0.243 | Lecture |
Astronomy 101 | 4005 | 0.204 | 0.422 | Lecture |
Dance 101 | 2508 | 0.116 | 0.192 | Small tutorials |
Economics 101 | 15,340 | 0.102 | 0.411 | Lecture |
Psychology 202 | 12,000 | 0.104 | 0.403 | Remote |
Sociology 202 | 8200 | 0.117 | 0.379 | Lecture |
English 101 | 3200 | 0.122 | 0.361 | Recorded online lectures |
Spanish 191 | 7300 | 0.124 | 0.342 | Recorded online lectures |
Introduction to social network analysis
To appreciate the nuances of this tool, individuals should understand the fundamentals of social network analysis. Managers, academics, and students can use this tool, even if they do not understand social network analysis, but might overlook some of the subtleties.
Social network analysis comprises a series of tools to explore how information, resources, friendships, and other attributes spread across networks of people, teams, organizations, or communities—such as students and courses. These tools include graphs, similar to the following example and a range of metrics to characterise these graphs. To illustrate,
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each circle, called a node or vertex, could represent a person, team, or community; in the following graph, each node represents a course or a student.
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each line or arrow, called an edge or tie, represents the association between these nodes; in the following graph, each edge indicates that a student is enrolled in a particular course.
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the various colours could represent some attribute or characteristic, such as whether the students are majoring in science of humanities
IIn this graph, most of the students had enrolled in C4—the fourth course. This simplified graph indicates that, perhaps, C4 introduced students who would otherwise not meet to one another.
This simplified graph is simple to interpret. But realistic graphs, potentially comprising hundreds of courses, thousands of students, and many thousands of connections, are hard to interpret. Therefore, after researchers construct these graphs, they can utilise software to calculate a range of metrics or measures. Some of the metrics impart key information about each node—in this instance, each course or student—sometimes called positional metrics. These metrics are often called measures of centrality, because they demonstrate the significance or centrality of each node or person to the network. To illustrate
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one metric, called betweenness centrality, measures the extent to which a node, course, or student seems to bridge distinct segments of the network, such as distinct academic disciplines. If the betweenness centrality of a course is high, perhaps diverse students, who would otherwise not meet, might enrol in this course.
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another metric, called eigenvalue centrality, measures the degree to which each node, course, or student is connected to nodes that are also connected to many nodes. For example, this measure could indicate whether a student has developed a relationship with the most connected peers.
Other metrics gauge characteristics of the entire network. For instance
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density, one common metric, refers to the proportion of nodes that are connected to other nodes
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for example, if density is 0.4, 40% of all pairs of nodes are connected to one another
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values above 0.2 typically indicate the nodes are strongly connected to each other
Researchers can utilize a variety of software tools to conduct social network analysis. For example, they can use the packages igraph, readr, haven, and gplot2 in R. For more information, see this link. Or they can utilize other specialist tools, such as NetworkX in Python. In essence, researchers merely need to
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install the software
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upload the data, such as an Excel or csv file
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write or adapt some code
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analyze the metrics this code generates.
Most software tools that conduct social network analysis will generate a range of metrics, such as density, mean distance, transitivity, in-degree centrality, out-degree centrality, betweenness centrality, and eigenvalue centrality depending on the features of this network.
Student-course bipartite networks: Example
One example of social network analysis that is applicable to tertiary education is called student-course bipartite networks. This network includes two kinds of notes—students and courses—and is thus referred to as bipartite. In the following table
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the degree centrality of a course is actually the total number of students to which this course is connected divided by the total number of students to which this course could be connected. If degree centrality is high, students are more likely to meet each other in these courses
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the local clustering coefficient of a course represents the degree to which this course connects students who would otherwise not be connected; low numbers indicate the course is especially likely to connect students who otherwise would not be connected
Course | Number of enrolled students | Degree centrality | lLocal clustering coefficient | Format |
|---|---|---|---|---|
Statistics 101 | 20,300 | 0.243 | 0.243 | Lecture |
Astronomy 101 | 4005 | 0.204 | 0.422 | Lecture |
Dance 101 | 2508 | 0.116 | 0.192 | Small tutorials |
Economics 101 | 15,340 | 0.102 | 0.411 | Lecture |
Psychology 202 | 12,000 | 0.104 | 0.403 | Remote |
Sociology 202 | 8200 | 0.117 | 0.379 | Lecture |
English 101 | 3200 | 0.122 | 0.361 | Recorded online lectures |
Spanish 191 | 7300 | 0.124 | 0.342 | Recorded online lectures |
ITo illustrate how tertiary institutions could utilize these networks, Israel et al. (2022) utilized a dataset, from the University of Michigan, that stipulates all the courses in which students had enrolled during particular years. The dataset also stored other information, such as the credit hours, format, and pre-requisites of each course. The researchers utilized NetworkX to generate a graph and the following table. To demonstrate how to interpret this table
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many students enrolled in Statistics 101, increasing the degree centrality. More interestingly, the local clustering coefficient of his course is low, suggesting that many of these students would not have met if they had never enrolled in this course
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fewer students enroll in Astronomy 101. Nevertheless, the degree centrality is high because this course attracts diverse students. Admittedly, the local clustering coefficient is high too, indicating these students may have met otherwise, even if they had not enrolled in this class. Yet, because the class comprises smaller tutorials, rather than larger lectures, this class might have enhanced the quality of relationships
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although fewer students enroll in Dance 101, the local clustering coefficient is low, indicating these students would not have met otherwise.
Israel et al. (2022) also calculated the social network metrics of each student. For example, this analysis identified students who generated high levels of betweenness centrality. These students tend to connect peers—and thus may help students meet one another.
Student-course bipartite networks: Implications
Deans, discipline chairs, and other managers could utilize this network analysis to optimize their course. For example, according to Israel et al. (2022), managers could
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identify courses that are especially like to connect diverse students
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identify courses that are especially like to connect students who might be at risk of failure; that is, the managers could repeat the analysis, but utilize only a subset of students
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devote more resources to these courses—or even drop courses that do not connect students
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identify students who are disconnected—and perhaps offer these students more opportunities to connect to other students
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identify students who are especially connected—and perhaps assign these students roles in which they can support their peers.
If students are granted access to these tables, or a simplified variant, these individuals could utilize the data to choose courses in which they are likely to meet a range of diverse individuals.
References
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Baer, M. (2010). The strength-of-weak-ties perspective on creativity: a comprehensive examination and extension. Journal of Applied Psychology, 95(3).
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Fronczak, A., Mrowinski, M. J., & Fronczak, P. (2022). Scientific success from the perspective of the strength of weak ties. Scientific reports, 12(1).
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Israel, U., Koester, B. P., & McKay, T. A. (2020). Campus connections: student and course networks in higher education. Innovative Higher Education, 45(2), 135-151.
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Mehreen, A., Hui, Y., & Ali, Z. (2019). A social network theory perspective on how social ties influence perceived employability and job insecurity: evidence from school teachers. Social Network Analysis and Mining, 9(1), 1-17.