Is there a better algorithm to find connected clusters? - c++

Question

I'd like to find a better algorithm to find connected clusters.
For example, if I input:
(8, 6),
(1, 8),
(3, 5)
, then there are two connected clusters: <1,6,8> and <3,5>.
I tried to do that using Depth First Search, but it spent too much time (several days) when the inputs are very very substantial.
By the way, I tried to use igraph library; it was faster, but memory leak happened, my computer got breakdown.
My code (DFS) is below.
#ifndef GRAPH_I_H
#define GRAPH_I_H
#include <iostream>
#include <ctime>
#include <cmath>
#include <queue>
#include <mechsys/linalg/matvec.h>
using namespace std;
class Graph_i
{
public:
int NumOfFractures;
Array<Array<int>> G;
Array<int> Visited;
public:
Graph_i(const int NumOfFractures_1, const Array<int> Connections);
void DFS(int V, Array<int> &B);
void CreateGraph_i(Array<Array<int>> &S);
};
inline Graph_i::Graph_i(const int NumOfFractures_1, const Array<int> Connections)
{
NumOfFractures = NumOfFractures_1;
G.resize(NumOfFractures);
for (int i = 0; i < NumOfFractures; ++i)
G[i].resize(NumOfFractures);
for (int i = 0; i < NumOfFractures; ++i)
{
for (int j = 0; j < NumOfFractures; ++j)
G[i][j] = 0;
}
for (int i = 0; i < Connections.Size() / 2; ++i)
{
G[Connections[2 * i]][Connections[2 * i + 1]] = 1;
G[Connections[2 * i + 1]][Connections[2 * i]] = 1;
}
Visited.resize(NumOfFractures);
for (int i = 0; i < NumOfFractures; ++i)
{
Visited[i] = 0;
}
}
inline void Graph_i::DFS(int V, Array<int> &B)
{
Visited[V] = 1;
B.Push(V);
for (int i = 0; i < NumOfFractures; ++i)
{
if (Visited[i] == 0 && G[V][i] == 1)
DFS(i, B);
}
}
inline void Graph_i::CreateGraph_i(Array<Array<int>> &S)
{
if (S.Size() != 0)
{
std::cout << "Error! ListOfClusters should be empty array!\n";
exit(0);
}
for (int i = 0; i < NumOfFractures; ++i)
{
if (Visited[i] == 0)
{
Array<int> A;
DFS(i, A);
S.Push(A);
}
}
}
#endif
Main function (this is just one time loop; actually, in my code, there are many loops; and I have used OpenMP):
#include <Graph_i.h>
int main()
{
Array<int> Connections; //this is the input, containing pairs, e.g., 1,2,1,3,5,6; so, <1,2,3> is a connected cluster, <5,6> is also a cluster; so, I need algorithm to identify them
//size of this array can be very very large
Array< Array<int> > Listofclusters;// this two order array is used to recode connected clusters
Graph_i G(Connections.Size(), Connections);
G.CreateGraph_i(Listofclusters);
return 0;
}