Implementation Of A Hypergraph In C++

In this post, we will explore the application of a Hypergraph in C++. Prior to delving into its implementation details, it is essential to understand the concept of a Hypergraph.

What is the Hypergraph?

A hypergraph is a distinctive variation of a graph, enabling a single edge to link two or more vertices. This type of graph, known as a hypergraph, extends the concept by permitting a single edge to establish connections with multiple vertices.

The edge within the hypergraph is commonly known as the hyperedge. The representation of the hypergraph can be done using H(E, V), where E indicates a hyperedge and V represents the group of vertices linked by that specific hyperedge.

Example:

Let's consider an illustration to apply the hypergraph in C++ utilizing the map container. The group of nodes linked by an edge is kept as a value within the map, while the edge's identifier is kept as a key. Subsequently, we removed "edge2" from the hypergraph by employing the erase method. Furthermore, we incorporated "edge4" that connects the four vertices of the hypergraph using the insert method. Ultimately, all the edges of the hypergraph along with the nodes they connect have been displayed.

Code Implementation:

#include <bits/stdc++.h>
#include <iostream>
using namespace std;
void createHyperGraph() {
map<string, vector<int>> h_graph = {{"edge1", {42, 31, 82}},
                                        {"edge2", {31, 49, 62}},
                                        {"edge3", {48, 77}}};
h_graph.erase("edge2");
h_graph.insert({"edge4", {65, 87, 13, 29, 37}});
cout << "The hypergraph is :-" << endl;
for (auto ele : h_graph) {
string edge = ele.first;
cout << edge << " : ";
vector<int> vert = ele.second;
for (int v : vert) {
cout << v << " ";
}
cout << endl;
}
}
int main() {
createHyperGraph();
return 0;
}

Output:

Complexity Analysis:

Time complexity: O(N) to traverse all edges.

Space complexity: O(N) to store N edges.

Real-life use cases of Hypergraph

The first thing to consider when implementing the hypergraph over a regular graph is why it is necessary. Here, we'll look at a few real-world applications for hypergraphs.

• ✅ Social networks: The social network can be represented as a hypergraph. People can connect with friends, coworkers, family, and other relationships through social networks. As a result, we may utilize the graph's edges as relationships and its vertices as individual people. We can now consider the possibility that each relationship involves more than two people. For instance, there are four or five members of the family and ten friends.
• ✅ Database modelling: The hypergraph can be used to model a database if several table attributes need to be connected in a single relationship.
• ✅ Representation of a Complex System: The hypergraph is also useful for developing complex systems, including those involving biological interactions or transportation networks.

Types of Hypergraph

Several types of Hypergraph in C++. Some main types of Hypergraph are as follows:

• ✅ Uniform Hypergraphs: A uniform hypergraph has an equal number of vertices on each edge.
• ✅ Bipartite Hypergraphs: Bipartite hypergraphs have two disjoint sets for each vertex. Furthermore, every hyperedge has vertices from both sets.
• ✅ Directed Hypergraphs: Every hyperedge in a directed hypergraph has a direction. Thus, the order of related vertices in each hyperedge must be taken into account.
• ✅ Hypergraphs with Weights: Each vertex link can have a weight assigned to it so that the connections have varying degrees of significance.
• ✅ Hypergraphs with Labels: We can add a label to each of its connections to provide further details for a vertex.