Digraph – Definition, Examples and Activities

A digraph, short for a directed graph, is a mathematical concept used to represent relationships between objects. It consists of a set of vertices or nodes and a set of directed edges or arcs, indicating one-way connections between the vertices.

  • Unlike undirected graphs, where edges have no specific direction, digraph edges have an inherent orientation. This directional information is crucial for modeling systems with asymmetric relationships, such as dependencies, processes, or flows.
  • Algorithms like depth-first search and breadth-first search are often applied to analyze and traverse digraphs, making them a fundamental data structure in computational and mathematical contexts.
  • In a digraph, each edge has a specific direction, indicating a one-way connection between two nodes. This is different from an undirected graph, where edges have no direction, and the connection between nodes is bidirectional.
  • E is a set of directed edges or arcs, each connecting an ordered pair of vertices.
  • Digraphs are used in various fields, including computer science, network theory, biology, and social sciences, to model relationships and dependencies. They are a fundamental data strucature in algorithms and data representation.

For example, a social network can be represented as a digraph, where individuals are nodes and directed edges indicate the direction of friendships or connections between them. In a transportation network, vertices could represent locations, and directed edges could represent one-way roads or routes.

The study of digraphs involves understanding properties such as connectivity, cycles, and paths. Algorithms like depth-first search (DFS) and breadth-first search (BFS) are commonly applied to analyze and traverse digraphs.

Typical varieties of digraphs consist of:

  1. Consonant digraphs:
  2. Consonant pairs (such as “ch” in “chat”) that stand for a single sound.

  3. Vowel diagraphs:
  4. Vowel digraphs are vowel pairs that combine to form a single sound, such as “ai” in “rain”.

  5. Blends:
  6. Consonant and vowel digraph combinations (like “spl” in “splash”). These improve reading comprehension and phonemic awareness.

  7. Digraph Definition
  8. A combination of two letters that work together to spell a single sound is what is a Digraph.
    The five most common digraphs are ch-, sh-, th-, ph-, and wh-.

Digraph Word Origin

The digraph is a Greek word that actually describes two letters that come together. “di” implies two, and “graph” implies written. So, the word digraph means something that is written that has two parts.

The Story of Digraphs

When Rick and Bonnie get together, they are able to pronounce their individual sounds, “B” and “R,” as in “broom” and “brown.” Rick lives next door to Bonnie.

Both the b and the r sounds are audible.
On the other hand, when Cathy and Harry get together and each says their sound out loud, /k/ like in cat and /h/ like in horse, it sounds weird.

They thus made the decision to band together to create a new /ch/ sound, such as in each, chat, and chip. And, when this happens, part ch is called a digraph.
You can see that the two letters c and h came together to spell the single sound /ch/.

Digraph Examples

Digraphs can appear at the start, middle, or end of a word and make initial sounds. Every sound, along with its applications as an initial and final digraph, a few digraph examples are listed below.


Initial or Final Sound




chair, cheese, child



lunch, pinch, rich



luck, sick, tuck



knight, knife, knot



phone, phonics, phrase



shape, ship, shoe



brush, dish, flash



bliss, chess, mess



think, three, thumb



bath, earth, with



whale, what, why



wreck, wrist, writing

There are two different kinds of digraphs, to start. The heterogeneous digraph is the most prevalent type. That is, it’s made up of two different letters, like “ck” or “sh.” We also have homogenous digraphs that are made up of two of the same letters, like “ss.”

Why are digraphs important?

Introducing directed graphs, also known as digraphs, to kids is a great way to help them learn because it fosters critical thinking, helps them develop basic cognitive abilities, and sets the foundation for more complex mathematical ideas. Here’s why are digraphs important:

  1. Visual Representation:
  2. Digraphs provide a visual and concrete way for children to understand and represent relationships. The arrows in digraphs help illustrate the direction of connections, aiding in visual comprehension.

  3. Logical Reasoning:
  4. Understanding the directional nature of edges in digraphs promotes logical reasoning skills. Children learn to follow and predict sequences, which is foundational for problem-solving and decision-making.

  5. Pattern Recognition:
  6. Recognizing patterns is a key aspect of early childhood education. Digraphs help children identify and understand patterns in the arrangement of vertices and edges, fostering a deeper understanding of order and structure.

  7. Introduction to Graph Theory:
  8. While it may sound sophisticated, introducing basic graph theory concepts through digraphs at an early age can spark interest in mathematics and computer science. It sets the stage for more advanced topics in these fields.

  9. Real-World Applications:
  10. Many real-world scenarios involve directional relationships, and understanding digraphs can help children interpret and analyze these situations. Examples such as maps, family trees, and process flows can be effectively modeled using digraphs.

Incorporating digraphs into early education not only facilitates mathematical and logical skills but also encourages a playful and creative approach to learning. As a result, children develop a strong foundation for more complex mathematical concepts while enjoying the interactive and visually engaging nature of digraphs.

How many digraphs are there?

In written English, there are thought to be more than 125 digraphs.
The count may be reasonable for a small number of vertices, but as the graph gets larger, there are a huge number of possible digraphs. Multiple outgoing edges can exist for each vertex, creating an enormous combinatorial array of possible combinations.

While specific methods may vary, EuroKids likely employ hands-on and interactive activities to teach digraphs. Activities include using visual aids, games, and storytelling to illustrate directional relationships between objects. Incorporating fun and engaging exercises helps children grasp the concept of digraphs in a practical and memorable way.

In EuroKids, teachers might utilize colorful charts, flashcards, and interactive games to introduce digraphs like “ch,” “sh,” and “th.” Through storytelling and group activities, children may practice identifying and creating words with these digraphs. Such hands-on experiences aim to make learning enjoyable, fostering a solid foundation in language skills.

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