What is Hypergraph?
A hypergraph is a generalization of a graph, where an edge can connect any number of vertices. In a hypergraph, each edge is called a hyperedge and can connect any number of vertices, instead of just two vertices like in a traditional graph.
A hypergraph is represented by H(E, V) where E is the HyperEdge and V is the value linked with that edge.
To know more about the Hypergraph, refer here.
How to implement a Hypergraph in C++?
To implement a hypergraph, we can use you can use a map. Follow the steps mentioned below to implement a hypergraph in C++:
- Create a map to store the hyperedges and their associated vertices.
- The key for the unordered_map can be a string representing the name of the hyperedge, and
- The value can be a vector containing the vertices that the hyperedge is connected to.
Below is the C++ code to implement the hypergraph:
C++
// C++ Implementation of the above graph#include <bits/stdc++.h>#include <iostream>using namespace std;// #include <string>// #include <vector>// Function to create Hypergraphvoid hyperGraph(){ // Define a hypergraph with 3 hyperedges // and 6 vertices map<string, vector<int> > hypergraph = { { "e1", { 1, 2, 3 } }, { "e2", { 3, 4, 5 } }, { "e3", { 2, 4, 6 } } }; // Add a new hyperedge hypergraph.insert({ "e4", { 1, 5, 6 } }); // Remove a hyperedge hypergraph.erase("e2"); // Modify a hyperedge hypergraph["e1"] = { 1, 2 }; // Print the hypergraph cout << "Hypergraph:" << endl; for (auto a : hypergraph) { string edge = a.first; cout << edge << " : "; vector<int> vertices = a.second; for (int vertex : vertices) { cout << vertex << " "; } cout << endl; }}// Driver Codeint main(){ // Function call hyperGraph(); return 0;} |
Java
// Java Implementation of the above graphimport java.io.*;import java.util.*;class GFG { // Function to create Hypergraph static void hyperGraph() { // Define a hypergraph with 3 hyperedges // and 6 vertices Map<String, List<Integer> > hypergraph = new HashMap<>(); hypergraph.put("e1", Arrays.asList(1, 2, 3)); hypergraph.put("e2", Arrays.asList(3, 4, 5)); hypergraph.put("e3", Arrays.asList(2, 4, 6)); // Add a new hyperedge hypergraph.put("e4", Arrays.asList(1, 5, 6)); // Remove a hyperedge hypergraph.remove("e2"); // Modify a hyperedge hypergraph.put("e1", Arrays.asList(1, 2)); // Print the hypergraph System.out.println("Hypergraph:"); for (Map.Entry<String, List<Integer> > entry : hypergraph.entrySet()) { String edge = entry.getKey(); System.out.print(edge + " : "); List<Integer> vertices = entry.getValue(); for (int vertex : vertices) { System.out.print(vertex + " "); } System.out.println(); } } public static void main(String[] args) { // Function call hyperGraph(); }}// This code is contributed by lokeshmvs21. |
Python3
# Python Implementation of the above graph# Function to create Hypergraphdef hyper_graph(): # Define a hypergraph with 3 hyperedges # and 6 vertices hypergraph = { "e1": [1, 2, 3], "e2": [3, 4, 5], "e3": [2, 4, 6], } # Add a new hyperedge hypergraph["e4"] = [1, 5, 6] # Remove a hyperedge del hypergraph["e2"] # Modify a hyperedge hypergraph["e1"] = [1, 2] # Print the hypergraph print("Hypergraph:") for edge, vertices in hypergraph.items(): print(f"{edge}: {vertices}")# Function callhyper_graph()# This code is contributed by manav23lohani. |
C#
// C# Implementation of the above graphusing System;using System.Collections.Generic; class GFG { // Function to create Hypergraph static void hyperGraph() { // Define a hypergraph with 3 hyperedges // and 6 vertices Dictionary<string, List<int>> hypergraph = new Dictionary<string, List<int>>(); hypergraph.Add("e1", new List<int>{1, 2, 3}); hypergraph.Add("e2", new List<int>{3, 4, 5}); hypergraph.Add("e3", new List<int>{2, 4, 6}); // Add a new hyperedge hypergraph.Add("e4", new List<int>{1, 5, 6}); // Remove a hyperedge hypergraph.Remove("e2"); // Modify a hyperedge hypergraph["e1"] = new List<int>{1, 2}; // Print the hypergraph Console.WriteLine("Hypergraph:"); foreach(KeyValuePair<string,List<int>> entry in hypergraph) { string edge = entry.Key; Console.Write(edge + " : "); List<int> vertices=entry.Value; foreach (var vertex in vertices) { Console.Write(vertex + " "); } Console.WriteLine(); } } public static void Main() { // Function call hyperGraph(); }}// This code is contributed by Pushpesh Raj |
Javascript
// JavaScript Implementationfunction hyperGraph() { // Define a hypergraph with 3 hyperedges // and 6 vertices let hypergraph = { e1: [1, 2, 3], e2: [3, 4, 5], e3: [2, 4, 6] }; // Add a new hyperedge hypergraph['e4'] = [1, 5, 6]; // Remove a hyperedge delete hypergraph.e2; // Modify a hyperedge hypergraph.e1 = [1, 2]; // Print the hypergraph console.log('Hypergraph:'); for (let [edge, vertices] of Object.entries(hypergraph)) { console.log(`${edge} : ${vertices.join(' ')}`); }}// Driver CodehyperGraph(); |
Output
Hypergraph: e1 : 1 2 e3 : 2 4 6 e4 : 1 5 6
Time Complexity: O(N) // since we are traversing all the elements inside the unordered map using a for loop
Auxiliary Space: O(N) // since we are using an unordered map to store all the elements
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