Find Center of Star Graph

**Problem Statement:** Given the required input arguments, write an efficient algorithm to solve the **Find Center of Star Graph** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge. **Hint / Expected Approach:** Center appears in both first two edges **Edge Cases to Consider:** - (1) Star with 3 nodes - (2) All edges include center trivially - (3) Large star

Examples

Example 1

Input: [[1,2],[2,3],[4,2]]

Output: 2

Explanation: Center is 2

Example 2

Input: [[1,2],[5,1],[1,3]]

Output: 1

Explanation: Center is 1

Example 3

Input: [[1,2]]

Output: 1 or 2

Explanation: Two-node star (trivial)

Constraints

▪2 <= vertices <= 1000
▪0 <= edges <= 5000
▪Avoid infinite cycles during depth traversal

Watch Out For Edge Cases

▪Star with 3 nodes
▪All edges include center trivially
▪Large star

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