What Is Null Graph in Data Structure?


Larry Thompson

A null graph in data structure refers to a special type of graph that does not contain any edges or vertices. It is essentially an empty graph with no connections between any elements. In other words, it is a graph with zero nodes and zero edges.

Null graphs are often used as placeholders or as initial states for certain algorithms and data structures. They can serve as a starting point from which new nodes and edges can be added to create more complex graphs.

When representing a null graph visually, it is common to use the symbol Ø or simply an empty set {}. This clearly indicates that the graph is empty and devoid of any elements.

Properties of Null Graphs

No Vertices: As mentioned earlier, null graphs do not have any vertices. This means that there are no individual points or entities in the graph.

No Edges: Similarly, null graphs do not have any edges connecting vertices since there are no vertices present in the first place.

Applications of Null Graphs

Null graphs may not seem particularly useful on their own, but they play an important role in various areas of computer science and data structures. Here are a few examples:

1. Initialization:

In many cases, null graphs are used as initial states for algorithms or data structures. For example, when implementing a new graph data structure, creating an empty null graph serves as a starting point before adding actual nodes and edges.

2. Placeholder Values:

In some algorithms, null graphs act as placeholders for missing or undefined values. They can represent situations where there is no valid solution or where certain operations cannot be performed.

3. Testing Conditions:

Null graphs can be used to test conditions in algorithms or functions. By checking whether a graph is null, certain actions or computations can be triggered based on the absence of elements.


In summary, a null graph is an empty graph with no vertices or edges. It serves as a placeholder or initial state in various algorithms and data structures. While it may not have direct applications on its own, understanding null graphs is essential for building more complex graphs and solving problems in computer science.

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