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Mapping Course Prerequisites with Python: Visualizing Networks for Better Course Planning

Knowing course prerequisite is important for students to plan their study path. With a clear visual representation, navigating course pathways becomes easier, allowing students to plan their academic journey more effectively.

With the beginning of the new semester, today let’s explore how Python can be used to map out course prerequisite networks, providing both static and interactive visualizations that can aid in course planning.

To achieve this, we’ll demonstrate two methods: using NetworkX for static visualizations and ipysigma for interactive ones. Both tools help visualize networks, but each serves different purposes depending on the complexity and scale of the data.

Course prerequisites network visualization made with ipysigma

Course prerequisites network visualization made with ipysigma

 

Use Case: Course-Prerequisite Networks

In this example, we’ll visualize the course prerequisite network for undergraduate and postgraduate at HKUST for the 2024-25 academic year.

Installing Packages

To get started, we need to install the necessary libraries using pip:

!pip install pandas
!pip install networkx
!pip install matplotlib
!pip install ipysigma

 

Creating the Data

We start by creating a simple DataFrame to represent courses and their prerequisites.

import pandas as pd

# Define the data
data = {
    ‘Type’: [‘UG’, ‘UG’, ‘UG’, ‘UG’, ‘UG’, ‘UG’],
    ‘Dept’: [‘MATH’, ‘MATH’, ‘MATH’, ‘MATH’, ‘MATH’, ‘MATH’],
    ‘Course Code’: [‘MATH 1003’, ‘MATH 1012’, ‘MATH 1013’, ‘MATH 1014’, ‘MATH 1023’, ‘MATH 1024’],
    ‘Course Name’: [
        ‘Calculus and Linear Algebra’,
        ‘Calculus IA’,
        ‘Calculus IB’,
        ‘Calculus II’,
        ‘Honors Calculus I’,
        ‘Honors Calculus II’
    ],
    ‘Prerequisites’: [
        ‘None’,
        ‘None’,
        ‘None’,
        ‘MATH 1012, MATH 1013, MATH 1023, MATH 1003‘,
        ‘None’,
        ‘MATH 1023‘
    ]
}

# Create a DataFrame
df = pd.DataFrame(data)

# Display the DataFrame
df

 

Small Dataset For Testing

A simplified DataFrame to represent courses and their prerequisites

Creating the Graph with NetworkX

Using this DataFrame, we can create a directed graph in NetworkX. This involves adding nodes to represent the courses and edges to represent the course prerequisites.

import networkx as nx 

# Initialize a directed graph 
G = nx.DiGraph()

# Add nodes and edges from the dataframe 
for index, row in df.iterrows(): 
    course = row[‘Node_name’] 
    prerequisites = row[‘Prerequisites’] 
 
    # Add the course node 
    G.add_node(course, label=course)  # Add type and label to the node 

    # Add edges for prerequisites 
    if pd.notna(prerequisites) and prerequisites != ‘None’: 
        for prereq in prerequisites.split(‘,’): 
            prereq = prereq.strip() 
            G.add_node(prereq) 
            G.add_edge(prereq, course) 

# Draw the static network 
nx.draw(G, with_labels=True, font_size=5)
Networkx Representation With Small Dataset

Visual representation of the simplified DataFrame by NetworkX

While NetworkX helps create a structured visual representation of the network, static graphs can become difficult to interpret when dealing with large datasets. For example, when we load 3,000+ course records, the graph becomes difficult to interpret, requiring further customization.

Networkx Representation With Full Dataset

Visual representation of course prerequisites with NetworkX

Additionally, the static layout of the NetworkX visualization makes it challenging to interactively explore and analyze the network.

Enhancing with ipysigma

To address the limitations of static graphs, we can use ipysigma to create interactive visualizations that allow for dynamic exploration of the network. Instead of using the “draw” function in NetworkX, we use ipysigma’s Sigma function to generate an interactive widget.

From ipysigma import Sigma

# Create an ipysigma widget
sigma = Sigma(G) 

# Display the widget in the notebook 
display(sigma)

 

One of ipysigma’s key advantages is the ability to export the graph as an HTML file, making it easy to share interactive visualizations with others.

# Export the graph to an HTML file
sigma.write_html(G, ‘./sigma.html’, fullscreen=True)

 

 

Customizing with ipysigma

ipysigma also offers extensive customization options, allowing adjustments to the layout and appearance of the graph (updated html). You can control variables like node color, size, and edge types to make the visualization more informative. For more details, you can refer to the available visual variables in PyPi.

import ipysigma

# Export the graph to an HTML file
sigma.write_html(
    G,
    ‘./sigma_c.html’,
    fullscreen=True,
    node_color= ‘dept’,  # Use the ‘color’ attribute for course type
    node_size_range=(1, 15),
    default_edge_type=‘curve’,
    node_border_color_from=‘node’,
    default_node_label_size=12,
    edge_size_range=(1, 15),
    node_size=lambda node: G.degree(node)    
)

 

 

 

Remarks

By mapping course prerequisite networks, we can help students and academic advisors visualize the relationships between courses. While NetworkX is a powerful tool for creating these visualizations, its static nature may limit its effectiveness for complex datasets. ipysigma enhances this process by enabling interactive exploration, making it easier to navigate and understand large networks. This makes ipysigma a valuable addition to your toolkit when working with network data in an educational context.

All the code and the course prerequisite dataset can be found and run on Google Colab.

– By Ernest Lam, HKUST

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published September 4, 2024