Introduction to Tree Structure

Tree Terminologies

graph TD A --> B A --> C A --> D B --> E B --> F F --> J F --> K J --> M D --> G D --> H D --> I H --> L L --> N L --> O

  • Root: A node that has no incoming edge (no parent).
    Node $A$ is the root of the above tree.

  • Parent: A node $m$ is the parent of nodes $n_i$ if there are edges from $m$ to each $n_i$.
    Node $D$ is the parent of nodes $\{G, H, I\}$.

  • Child: A node $n$ is a child of node $m$ if there is an edge from $m$ to $n$.

  • Siblings: Nodes $\{n_i\}$ are siblings if they share the same parent node $m$.
    For example, $\{G, H, I\}$ are siblings.

  • Descendants: All nodes that can be reached from a given node by following downward edges (recursively).
    Nodes $\{J, K, M\}$ are descendants of node $F$.

  • Ancestors: All nodes on the path from a given node to the root (excluding the node itself).
    For example, ancestors of $M$ are $\{J, F, B, A\}$.

  • Degree of a Node: The number of children of that node (i.e., number of outgoing edges).
    Degree of node $D$ is $3$.
    Degree of a leaf node is $0$.

  • Degree of a Tree: The maximum number of children any node can have in a tree.
    Binary Tree has degree $2$ (i.e., each node in the tree has degree $\leq 2$).

  • Internal Node: A node with at least one child (degree $\geq 1$).
    Nodes $\{A, B, D, F, H, J, L\}$ are internal nodes.

  • External Node (Leaf Node): A node with no children (degree $0$).
    Nodes $\{C, E, G, I, K, M, N, O\}$ are leaf nodes.

  • Level: The level of a node is defined as the number of edges from the root to that node.
    Root is at level $0$.
    Node $F$ is at level $2$.
    Node $M$ is at level $4$.

  • Height of a Node: The number of edges in the longest downward path from that node to a leaf.
    Height of node $F$ is $2$ (path: $F \to J \to M$).

  • Height of a Tree: The height of the root node.
    Height of the above tree is $4$.

  • Forest: A collection of disjoint trees.
    If the root $A$ is removed, the remaining structure forms a forest of three trees rooted at ${B, C, D}$.