In a binary tree, the “degree” of a node refers to the number of connections it has. Specifically, the degree is determined by the count of edges linking the node to its parent and its children. Here’s a breakdown:
- Node Degree:
- A node with no children (a leaf) has a degree of 1.
- An internal node with one child has a degree of 2.
-
An internal node with two children has a degree of 3.
-
Tree Structure:
- The sum of all nodes’ degrees in a binary tree equals twice the number of edges, as each edge contributes to two nodes’ degrees.
-
For a tree with ( n ) nodes, there are ( n-1 ) edges, so the total degree is ( 2(n-1) ).
-
Average Degree:
- The average degree across all nodes in a binary tree can be calculated as ( \frac{2(n-1)}{n} = 2 – \frac{2}{n} ), which approaches 2 as the number of nodes increases.
In summary, the degree in a binary tree is a measure of how connected each node is, with leaves having the lowest degree and internal nodes typically having higher degrees.