Definition of a directed graph:
A directed graph, also known as a digraph, is a graph in which each edge of the graph has a direction associated with it. It means that each branch of the graph has a specific direction or orientation.

Explanation of the answer:
The correct answer is option 'D' - every branch. This means that in a directed graph, every branch or edge of the graph has a direction associated with it. Let's understand this in detail.

Understanding a directed graph:
In a directed graph, each edge or branch is represented by an arrow pointing from one vertex to another. The direction of the arrow indicates the relationship between the vertices. For example, if we have vertices A and B, and there is an arrow from A to B, it means that there is a directed edge from A to B.

Example:
Consider a simple directed graph with three vertices A, B, and C. The graph has three branches - AB, AC, and BC. In this case, each branch has a direction associated with it. The branch AB goes from vertex A to vertex B, AC goes from A to C, and BC goes from B to C.

Key points:
- In a directed graph, every branch or edge has a specific direction associated with it.
- This direction is indicated by an arrow pointing from one vertex to another.
- The direction of the arrow represents the relationship between the vertices connected by the edge.
- It is important to distinguish between directed graphs and undirected graphs, where the edges have no specific direction.

Conclusion:
In summary, a directed graph is a type of graph in which every branch or edge has a direction associated with it. The direction is indicated by an arrow pointing from one vertex to another. This property distinguishes directed graphs from undirected graphs and is essential for understanding the relationships and connections between the vertices in the graph.