Arc Diagrams: Examples, Types, Best Practices, and How to Build One

Arc diagrams are an intuitive way to visualize connections and relationships in your data, especially when the order of data points is important. They clarify how elements are linked while preserving sequence information, unlike more cluttered network graphs.

This guide covers everything you need to know about arc diagrams, from clear definitions and practical design tips to when to use them, how they work, and how to build your own, as well as their limitations.

What is an arc diagram?

An arc diagram is a type of data visualization where nodes, or data points, are laid out along a single axis. The connections between these nodes are then represented as semicircular arcs that are drawn above or below this axis. The key feature here is the linear arrangement of the nodes. This arrangement is not random; it follows a specific, meaningful order, such as chronological time, alphabetical sequence, or hierarchical ranking.

How does this differ from other network visualizations? A standard network graph, often called a force directed graph, places nodes in a two dimensional space where their position is determined by the connections between them. This is great for showing clusters and central nodes but loses any inherent order. A circular graph arranges nodes around a circle, which can be useful for showing cyclical patterns but can become messy. An adjacency matrix uses a grid to show every possible connection, which is powerful for dense networks but can be less intuitive to read at a glance.

Arc diagrams excel where these other types fall short. They masterfully reveal patterns and relationships while preserving the context of the node order. This makes them a unique and powerful tool for specific data storytelling scenarios. You can quickly see how entities connect across a sequence, making it a perfect choice when your data's order is as important as its connections.

When (and why) to use an arc diagram

Arc diagrams are not for every scenario, but when used appropriately, they provide clear visualization of connections where node order is key.

Here are the best scenarios for using an arc diagram:

• Ordered networks: Their greatest strength is visualizing networks where the node order is significant. This applies to data that follows a time series, a narrative sequence like chapters in a book, a ranked list, or any other defined progression.
• Adjacency and connection strength: They are excellent for showing which nodes are connected and, with some visual enhancements, how strong those connections are. Arc diagrams work best with smaller, more interpretable data sets where the goal is to understand direct relationships.
• Pattern detection: The linear layout makes certain patterns pop. You can easily spot repeated connections, nested links where smaller arcs are contained within larger ones, or symmetrical relationships between nodes.

The advantages of using an arc diagram are clear:

• Simplicity and clarity: They are often simpler and cleaner than a full network graph, especially for data that is not overly dense. This reduces visual clutter and makes the visualization easier to interpret.
• Preservation of sequence: The horizontal axis maintains the meaning of the node sequence, something that is lost in most other network layouts.
• Reduced edge crossings: Compared to force directed networks where connection lines can cross haphazardly, arc diagrams can offer a more organized view, though significant overlap is still a risk in dense networks.

However, arc diagrams are not always the answer. You should avoid them in these situations:

• Extremely dense networks: When you have a very large number of nodes and an even larger number of connections, an arc diagram can become a “hairball” of overlapping arcs, making it unreadable.
• When spatial layout is key: If your data has a geographic component or if the spatial relationship between nodes is critical, a map based visualization or a different graph layout would be more appropriate.

How arc diagrams work: The mechanics

Understanding arc diagrams begins with their core mechanics. At their simplest, arc diagrams use a straightforward structure you can adapt to suit your data and highlight the relationships that matter most.

Here is a breakdown of their structure:

• Nodes on an axis: The foundation is a single axis, typically horizontal, along which your nodes are placed. The order of these nodes is crucial and should be determined by a logical sorting principle relevant to your data.
• Connections as arcs: Relationships between nodes are drawn as semicircular arcs. An arc connects two nodes to show they are related. Typically, arcs are drawn above the axis, but they can also be placed below to represent different types of connections.
• Importance of node order: The power of an arc diagram comes from its ordered axis. You might sort nodes alphabetically for textual analysis, chronologically for time series data, by rank for hierarchical data, or by some other custom logic that provides context to the relationships you are showing.
• Directionality: A standard arc does not inherently show direction. To represent a directed link, from node A to node B but not vice versa, you might add an arrowhead to the arc or use color to distinguish the source from the target.
• Encoding connection strength: You can add more information to your arcs. A common technique is to vary the thickness or weight of the arc line to represent the strength or frequency of a connection. Thicker arcs indicate stronger relationships. Color intensity or saturation can achieve a similar effect.
• Self loops and bidirectional links: A self loop, where a node connects to itself, is typically shown as a small loop that starts and ends at the same node. For bidirectional links where A connects to B and B connects to A, you can either draw two separate arcs (one above and one below the axis) or use a single arc with arrowheads at both ends.

By understanding these components, you can begin to see how you can build an arc diagram that is not just a picture, but a detailed story about your data's structure and relationships.

Types and variants of arc diagrams

While basic arc diagrams are powerful, several variations can add clarity and detail. The best choice depends on your data and the story you want to tell. Here are some common types:

Basic arc diagrams

‍This is the simplest form, where arcs merely show the existence of a connection between two nodes. All arcs have the same color and thickness. It is perfect for answering the basic question: which nodes are connected?

Weighted arc diagrams

‍When you want to show the strength or frequency of connections, you can use a weighted arc diagram. In this variant, the thickness of the arc corresponds to a value. For example, in a diagram showing co-occurrence of characters in a novel, a thicker arc could represent more frequent interactions. This immediately draws the viewer's attention to the most significant relationships in the data set.

Color coded arc diagrams

‍Color is a fantastic tool for encoding categorical information. You can assign different colors to arcs to represent different types of connections. For instance, if you are visualizing communication patterns, you might use one color for emails, another for phone calls, and a third for meetings. This allows you to compare different categories of relationships within a single chart.

Bi-directional vs symmetrical arcs

‍Sometimes, the direction of a relationship matters. If you need to show both outgoing and incoming links, you can use a bi directional layout. This is often achieved by drawing one direction of connection above the axis and the opposite direction below it. This clearly separates the two flows, preventing visual confusion. Symmetrical arcs, on the other hand, are used when the relationship is mutual.

Vertical arc variants

‍Although less common, you can orient an arc diagram vertically. This can be a practical choice when you have many nodes and are constrained by horizontal space, such as in a narrow column of a report or on a mobile screen. The principles remain the same; nodes are just arranged along a vertical axis instead of a horizontal one.

Choosing the right variant is about matching the chart's features to your data's characteristics. If your data has weights, use a weighted diagram. If it has categories, use color. Your goal is always to make the final visualization as clear and informative as possible for your audience.

Design best practices and pitfalls

Designing an effective arc diagram is about more than plotting nodes and arcs. Smart design choices prevent confusion and improve insight. Here are the most important best practices and common pitfalls to watch for.

• Keep node order meaningful: This is the golden rule of arc diagrams. The order of nodes along the axis must have a clear and logical meaning. Be sure to explain this order to your audience so they can interpret the chart correctly.
• Avoid too many nodes or connections: Arc diagrams shine with moderate complexity. If your network has hundreds of nodes and thousands of connections, the chart will likely become an unreadable tangle of overlapping arcs. In such cases, consider filtering your data or choosing an alternative visualization.
• Use color wisely: Color can be used to group connection types, highlight specific arcs, or encode a quantitative value like connection strength. Use a limited, harmonious color palette to avoid overwhelming the viewer. Ensure your color choices are accessible to people with color vision deficiencies.
• Label nodes clearly: The horizontal layout of an arc diagram is a major advantage for labeling. There is ample space under each node for a clear, readable text label. Avoid rotating text or using tiny fonts.
• Manage overlapping arcs: Heavy overlap is the primary enemy of a clear arc diagram. If arcs are too crowded, consider filtering to show only the strongest connections, or group related links. Sometimes, adjusting the spacing between nodes can also help.
• Use axis gridlines or tick marks: Subtle tick marks or faint gridlines along the axis can help orient the reader and make it easier to trace arcs back to their corresponding nodes, especially in a wider chart.
• Don’t use it for spatial analysis: Remember, the position of nodes in an arc diagram is abstract and based on a chosen order. If the actual geographic or spatial location of your nodes is important, use a map or a different type of graph where node position is meaningful.

By keeping these tips in mind, you can design arc diagrams that are not only visually appealing but also highly effective at communicating complex relationships in an ordered context.

Examples and storytelling tips

Arc diagrams, when used effectively, transform lists of connections into clear narratives about patterns and relationships. Here are several examples and tips for telling compelling stories with arc diagrams.

Example 1: Visualizing character interactions in a story

‍Imagine you want to visualize how often characters in a book appear in the same chapter. You can line up the characters along the horizontal axis in the order of their first appearance. An arc between two characters shows they appeared in the same chapter. The thickness of the arc could represent the number of chapters they shared. This could reveal main character groupings, rivalries, or characters who bridge different storylines.

Example 2: Revealing gene co expression patterns

‍In genomics, you could arrange genes along an axis according to their position on a chromosome. An arc between two genes could indicate that they are co-expressed, meaning they are turned on or off at the same time. The color of the arc could represent the strength of the correlation. This could help scientists quickly identify clusters of functionally related genes.

Example 3: Showing patterns in website user journeys

‍You could visualize the flow of users through a website by placing pages along the axis in a logical order (e.g., home, products, about, contact). An arc could show the number of users who navigated from one page to another. This would quickly highlight common user paths, dead ends, or unexpected navigation loops.

Here are some tips for telling a story with your arc diagram:

• Lead with the node order: Start by explaining how you arranged the nodes on the axis. This provides the foundational context your audience needs to understand the chart. Is it chronological? Alphabetical? By importance?
• Highlight key connections: Use visual cues like thicker lines or brighter colors to draw attention to the most important or frequent connections. Guide your audience's eyes to the main event.
• Point out interesting patterns: Look for and explain patterns like nested relationships, where a series of short distance connections are contained within a single long distance one. Also, look for symmetries, where two nodes share a similar pattern of connections with other nodes.
• Use annotations: Don't be afraid to add text directly onto the chart to call out a specific arc or a group of nodes. An annotation like “Main character group” or “Unexpected connection” can add immense value.

Your goal is to guide your audience through the visualization, helping them see the same insights you discovered in the data.

How to create an arc diagram

You can create an arc diagram with a structured approach and the right data and tools. The process is straightforward once you understand the steps.

First, let's talk about data requirements. You will need two main things:

1. A node list that includes a unique identifier for each node and the value you will use to sort them along the axis.
2. A connection list, also known as an edge list. This is a list of pairs of nodes that are connected. Optionally, this list can include a weight for each connection (for a weighted arc diagram) or a category (for a color coded one).

Once your data is prepared, you can use various tools to build the visualization.

• Programming libraries: For coders, libraries in Python and JavaScript are popular choices.
  
  • Python: Libraries like Matplotlib can be used with NetworkX to generate arc diagrams. You would use NetworkX to manage the graph data and Matplotlib to draw the nodes and arcs. There are also specialized libraries that simplify the process.
  • JavaScript: The D3.js library is the gold standard for creating custom, interactive web based visualizations, including arc diagrams. It offers flexibility to control every visual aspect of the chart.
• BI and data visualization platforms: Some business intelligence platforms (such as Domo) support arc diagrams as a native chart type or allow you to import custom visuals. If your platform supports scripting (like R or Python), you can often generate an arc diagram within that environment.

Here is a general step by step process:

1. Prepare the data: Start by creating your node and connection lists. Ensure your node list is sorted according to the order you want to display on the axis.
2. Map the node positions: Assign each node a coordinate on the horizontal axis based on its sorted position.
3. Draw the arcs: For each connection in your list, calculate the geometry of the arc. An arc is essentially a semicircle where the diameter is the distance between the two connected nodes on the axis. The center of the semicircle will be the midpoint between the two nodes.
4. Assign arc attributes: If you are creating a weighted or colored diagram, apply the appropriate thickness or color to each arc based on your data.
5. Render the final chart: Draw the nodes, the arcs, the axis, and the labels. Add a title, a legend explaining any colors or weights, and any other necessary context.

For interactive dashboards, consider adding features like a hover effect that highlights a node and all its connections, or filters that allow users to show or hide certain categories of arcs. This can make a complex diagram much more explorable.

Limitations and when to use alternatives

Arc diagrams are effective, but they do have limitations. It is important to know when another type of visualization is a better fit.

The primary limitation is scalability. Arc diagrams are not well suited for very large or very dense networks. With hundreds of nodes or thousands of connections, the chart quickly becomes cluttered with overlapping arcs, a phenomenon often called a “hairball.” This makes it impossible to trace individual connections or discern patterns.

Another limitation is that arc diagrams do not inherently convey directionality well. While you can add arrowheads or use colors, these solutions can add to the visual clutter and may not be as intuitive as layouts designed specifically for directed graphs.

So, when should you use an arc diagram alternative?

• Traditional network graphs (force directed): If you need to visualize the community structure or topology of a complex, dense network, a force directed layout is a better choice. These algorithms position nodes based on their connections, pulling strongly connected nodes together and pushing apart unrelated ones.
• Adjacency matrix: For very dense networks where you need to see every possible connection (or lack thereof), an adjacency matrix is ideal. It uses a grid where each cell represents a potential connection. This is less intuitive for seeing paths but excellent for a detailed, comprehensive overview.
• Sankey diagrams: If your goal is to show the flow of quantities between nodes, a Sankey diagram is far superior. It uses the width of the flow paths to represent volume, making it perfect for visualizing things like energy flow, budget allocations, or user journeys with conversion rates.
• Parallel coordinate plots: When your data has many different dimensions or attributes for each node, and you want to see patterns across these attributes, a parallel coordinate plot can be a good alternative. It allows you to see how different nodes cluster based on their attributes rather than their direct connections.

The key is to choose the visualization that best answers the question you are asking of your data. If that question is about connections within an ordered sequence, the arc diagram is your friend. If the question is about something else, do not hesitate to explore other options.

Conclusion and key takeaways about arc diagrams

Arc diagrams offer a clear way to visualize relationships within ordered data, making patterns and connections easy to see without added complexity. They work best for moderate data sets where node order carries meaning.

For a successful arc diagram, use a meaningful node order, clear labels, and visual elements like color and line weight to add information. Only use arc diagrams when node order matters and the network is not overly complex.

This guide gives you the tools to create effective arc diagrams that make data connections clear and actionable.

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