Working with Graphs & Trees

The fundamental distinction between graphs and trees is: 1) Trees are hierarchical structures with a single root node, while graphs can have any structure, 2) Trees cannot contain cycles (acyclic), while graphs can have cycles, 3) Every node in a tree (except root) has exactly one parent, while graph nodes can have multiple connections, 4) Trees have n-1 edges for n nodes, graphs can have any number of edges, 5) Trees have clear parent-child relationships, graphs have general vertex-edge relationships, 6) Tree traversal always has a clear starting point (root), graph traversal can start anywhere, 7) Trees are a specific type of directed acyclic graph (DAG), 8) Understanding this difference is crucial for choosing the right data structure for specific problems.