A planar graph has several useful properties that make it useful in a variety of applications. One common use for planar graphs is in network analysis and design. For example, in telecommunications, planar graphs can be used to model and analyze the connectivity of a network, such as the relationships between different components of a computer network or the relationships between different nodes in a communication network.

In contrast, a plane graph is mainly used as a visual representation of a graph, such as in graph theory, where it is important to see the relationships between different nodes in a graph.

It is not that one cannot use a plane graph for the applications of a planar graph or vice versa, but rather that planar graphs are more well-suited for certain applications because of their properties, while plane graphs may be used more for visual representation and illustration.
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