A connected, simple graph that has no cycles is called a tree. In graph theory, a tree has several important properties:

1. Acyclic: It contains no cycles.
2. Connected: There is a path between any two vertices.
3. n-1 Edges: If the tree has $n$ vertices, it will have $n-1$ edges.
4. Unique Path: There is exactly one path between any two vertices.

Would you like more details or have any questions about this concept?

Here are some related questions:

1. What is a spanning tree of a graph?
2. How do you find the minimum spanning tree of a weighted graph?
3. Can a tree have multiple connected components?
4. How does a binary tree differ from a general tree?
5. What is a rooted tree?
6. How can you represent a tree using adjacency lists or matrices?
7. What are some common algorithms for traversing trees?
8. How is the concept of a tree used in computer science?

Tip: When dealing with graphs, visualizing them can greatly help in understanding their properties and solving related problems.