Graph:

1. Cycles: May contain cycles (paths where the start and end nodes are the same).
2. Connectivity: Can be connected or disconnected.
3. Edges: Number of edges can exceed $V-1$ (where $V$ is the number of vertices).
4. Root: Does not have a designated root node.
5. Traversal: Traversal can be complex with multiple paths and cycles (e.g., BFS, DFS).

Tree:

1. Cycles: Always acyclic (no cycles).
2. Connectivity: Always connected (there is a path between any pair of nodes).
3. Edges: Always has exactly $V-1$ edges.
4. Root: Has a single root node from which all other nodes are reachable.
5. Traversal: Traversal is simpler and often involves methods like pre-order, in-order, and post-order