Mutual Friends using Graph Data Structure

Question

I’m trying to implement a mutual friends feature using a graph data structure represented as an adjacency list in Python. Each node represents a person, and each edge represents a friendship (an undirected connection).

For example: John — A, B, C, D
David — B, C, E, F The mutual friends of John and David should be B and C.

What I Want to Improve ->I want to make this more efficient for larger networks (e.g., thousands of nodes). -> I’d like to know if there’s a better graph representation or built-in library that simplifies this task. ->How can I extend this to find mutual friends among more than two users (e.g., common friends of John, David, and Alex)?

trincot · Accepted Answer · 2025-10-10 18:24:31Z

1

You can use set intersection:

adj = {
    "John": set(["A", "B", "C", "D"]),
    "David": set(["B", "C", "E", "F"]),
    "Helen": set(["A", "C", "D", "F"]),
}

print(adj["John"].intersection(adj["David"]))  # {'C', 'B'}
print(adj["John"].intersection(adj["David"], adj["Helen"]))  # {'C'}

The & set operator can be used as well:

print(adj["John"] & adj["David"])  # {'C', 'B'}
print(adj["John"] & adj["David"] & adj["Helen"])  # {'C'}

answered Oct 10 at 18:24

trincot

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4 Comments

Durga Oct 11 at 19:15

ok....tq.... is there any other solution for this

trincot Oct 11 at 19:39

Yes, you can write your own implementation of intersection. But I see no good reason to do that when the language offers you a native intersection method.

Durga Oct 11 at 20:59

actually i am not asking about the coding part....about the solution logic

trincot Oct 12 at 7:01

But you want the intersection, right? So what more do you expect than doing an intersection? Can you clarify more precisely what you look for?

Mohammad Othman · Accepted Answer · 2025-11-14 16:51:59Z

As trincot said : set intersection is the best way to do that.

If you want to use a graph, you could represents each person with a node and the friendship as edges connecting between the person and their friends.

To catch the mutual friends between X and Y , you could consider the outdegree of X and Y nodes, afterwards the intersection.

The full code will be:

class FriendshipGraph:
    def __init__(self):
        self.graph = defaultdict(set)

    def add_friendship(self, person1, person2):
        self.graph[person1].add(person2)
        self.graph[person2].add(person1)

    def get_mutual_friends(self, *people):
        if not people:
            return set()

        mutual_friends = self.graph[people[0]].copy()

        for person in people[1:]:
            if person not in self.graph:
                return set()
            mutual_friends &= self.graph[person]

        mutual_friends -= set(people)

        return mutual_friends


graph = FriendshipGraph()

Test the code with those examples:

graph = FriendshipGraph()

graph.add_friendship("Ahmed", "Mohammed")
graph.add_friendship("Ahmed", "Khaled")
graph.add_friendship("Ahmed", "Sara")
graph.add_friendship("Mohammed", "Khaled")
graph.add_friendship("Mohammed", "Fatima")
graph.add_friendship("Sara", "Fatima")
graph.add_friendship("Khaled", "Sara")
graph.add_friendship("Khaled", "Nour")
graph.add_friendship("Sara", "Nour")

print("Mutual friends between Ahmed and Mohammed:", graph.get_mutual_friends("Ahmed", "Mohammed"))

print("Mutual friends between Ahmed and Fatima:", graph.get_mutual_friends("Ahmed", "Fatima"))

print("Mutual friends between 3 people:", graph.get_mutual_friends("Ahmed", "Mohammed", "Sara"))

print("Mutual friends between 4 people:", graph.get_mutual_friends("Ahmed", "Mohammed", "Sara", "Fatima"))

print("Mutual friends between 5 people:", graph.get_mutual_friends("Ahmed", "Mohammed", "Sara", "Khaled", "Nour"))

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