Difference between Trees and Graphs

Trees Graphs
Path Tree is special form of graph i.e. minimally connected graph and having only one path between any two vertices. In graph there can be more than one path i.e. graph can have uni-directional or bi-directional paths (edges) between nodes
Loops Tree is a special case of graph having no loops, no circuits and no self-loops. Graph can have loops, circuits as well as can have self-loops.
Root Node In tree there is exactly one root node and every child have only one parent. In graph there is no such concept of root node.
Parent Child relationship In trees, there is parent child relationship so flow can be there with direction top to bottom or vice versa. In Graph there is no such parent child relationship.
Complexity Trees are less complex then graphs as having no cycles, no self-loops and still connected. Graphs are more complex in compare to trees as it can have cycles, loops etc
Types of Traversal Tree traversal is a kind of special case of traversal of graph. Tree is traversed in Pre-Order, In-Order and Post-Order (all three in DFS or in BFS algorithm) Graph is traversed by DFS: Depth First Search and in BFS : Breadth First Search algorithm
Connection Rules In trees, there are many rules / restrictions for making connections between nodes through edges. In graphs no such rules/ restrictions are there for connecting the nodes through edges.
DAG Trees come in the category of DAG : Directed Acyclic Graphs is a kind of directed graph that have no cycles. Graph can be Cyclic or Acyclic.
Different Types Different types of trees are : Binary Tree , Binary Search Tree, AVL tree, Heaps. There are mainly two types of Graphs : Directed and Undirected graphs.
Applications Tree applications : sorting and searching like Tree Traversal & Binary Search. Graph applications : Coloring of maps, in OR (PERT & CPM), algorithms, Graph coloring, job scheduling, etc.
No. of edges Tree always has n-1 edges. In Graph, no. of edges depend on the graph.
Model Tree is a hierarchical model. Graph is a network model.