Find Center of Star Graph in Python

Suppose we have one undirected star graph with n nodes labeled from 1 to n. As we know a star graph is a graph where there is one center node and exactly n - 1 edges that connect the center node with every other node. We have to find the center of the given star graph.

So, if the input is like

then the output will be 3 as 3 is at center.

To solve this, we will follow these steps −

• seen := a new set

• for each edge (u,v) in graph, do

  • if u is in seen, then

    • return u

  • if v is in seen, then

    • return v

  • insert u into seen

  • insert v into seen

Example

Let us see the following implementation to get better understanding −

def solve(graph):
   seen = set()

   for u,v in graph:
      if u in seen:
         return u
      if v in seen:
         return v
      seen.add(u)
      seen.add(v)

graph = [(1,3),(2,3),(4,3),(5,3),(6,3)]
print(solve(graph))

Input

[(1,3),(2,3),(4,3),(5,3),(6,3)]

Output

3