Graph implementation C++

Question

I was wondering about a quick to write implementation of a graph in c++. I need the data structure to be easy to manipulate and use graph algorithms(such as BFS,DFS, Kruskal

Answer 1

This question is ancient but for some reason I can't seem to get it out of my mind.

While all of the solutions do provide an implementation of graphs, they are also all very verbose. They are simply not elegant.

Instead of inventing your own graph class all you really need is a way to tell that one point is connected to another -- for that, std::map and std::unordered_map work perfectly fine. Simply, define a graph as a map between nodes and lists of edges. If you don't need extra data on the edge, a list of end nodes will do just fine.

Thus a succinct graph in C++, could be implemented like so:

using graph = std::map<int, std::vector<int>>;

Or, if you need additional data,

struct edge {
    int nodes[2];
    float cost; // add more if you need it
};

using graph = std::map<int, std::vector<edge>>;

Now your graph structure will plug nicely into the rest of the language and you don't have to remember any new clunky interface -- the old clunky interface will do just fine.

No benchmarks, but I have a feeling this will also outperform the other suggestions here.

NB: the ints are not indices -- they are identifiers.

Answer 2

I prefer using an adjacency list of Indices ( not pointers )

typedef std::vector< Vertex > Vertices;
typedef std::set <int> Neighbours;


struct Vertex {
private:
   int data;
public:
   Neighbours neighbours;

   Vertex( int d ): data(d) {}
   Vertex( ): data(-1) {}

   bool operator<( const Vertex& ref ) const {
      return ( ref.data < data );
   }
   bool operator==( const Vertex& ref ) const {
      return ( ref.data == data );
   }
};

class Graph
{
private :
   Vertices vertices;
}

void Graph::addEdgeIndices ( int index1, int index2 ) {
  vertices[ index1 ].neighbours.insert( index2 );
}


Vertices::iterator Graph::findVertexIndex( int val, bool& res )
{
   std::vector<Vertex>::iterator it;
   Vertex v(val);
   it = std::find( vertices.begin(), vertices.end(), v );
   if (it != vertices.end()){
        res = true;
       return it;
   } else {
       res = false;
       return vertices.end();
   }
}

void Graph::addEdge ( int n1, int n2 ) {

   bool foundNet1 = false, foundNet2 = false;
   Vertices::iterator vit1 = findVertexIndex( n1, foundNet1 );
   int node1Index = -1, node2Index = -1;
   if ( !foundNet1 ) {
      Vertex v1( n1 );
      vertices.push_back( v1 );
      node1Index = vertices.size() - 1;
   } else {
      node1Index = vit1 - vertices.begin();
   }
   Vertices::iterator vit2 = findVertexIndex( n2, foundNet2);
   if ( !foundNet2 ) {
      Vertex v2( n2 );
      vertices.push_back( v2 );
      node2Index = vertices.size() - 1;
   } else {
      node2Index = vit2 - vertices.begin();
   }

   assert( ( node1Index > -1 ) && ( node1Index <  vertices.size()));
   assert( ( node2Index > -1 ) && ( node2Index <  vertices.size()));

   addEdgeIndices( node1Index, node2Index );
}

Answer 3

The most common representations are probably these two:

• Adjacency list

• Adjacency matrix

Of these two the adjacency matrix is the simplest, as long as you don't mind having a (possibly huge) n * n array, where n is the number of vertices. Depending on the base type of the array, you can even store edge weights for use in e.g. shortest path discovery algorithms.

Answer 4

It really depends on what algorithms you need to implement, there is no silver bullet (and that's shouldn't be a surprise... the general rule about programming is that there's no general rule ;-) ).

I often end up representing directed multigraphs using node/edge structures with pointers... more specifically:

struct Node
{
    ... payload ...
    Link *first_in, *last_in, *first_out, *last_out;
};

struct Link
{
    ... payload ...
    Node *from, *to;
    Link *prev_same_from, *next_same_from,
         *prev_same_to, *next_same_to;
};

In other words each node has a doubly-linked list of incoming links and a doubly-linked list of outgoing links. Each link knows from and to nodes and is at the same time in two different doubly-linked lists: the list of all links coming out from the same from node and the list of all links arriving at the same to node.

The pointers prev_same_from and next_same_from are used when following the chain of all the links coming out from the same node; the pointers prev_same_to and next_same_to are instead used when managing the chain of all the links pointing to the same node.

It's a lot of pointer twiddling (so unless you love pointers just forget about this) but query and update operations are efficient; for example adding a node or a link is O(1), removing a link is O(1) and removing a node x is O(deg(x)).

Of course depending on the problem, payload size, graph size, graph density this approach can be way overkilling or too much demanding for memory (in addition to payload you've 4 pointers per node and 6 pointers per link).

A similar structure full implementation can be found here.

Answer 5

There can be an even simpler representation assuming that one has to only test graph algorithms not use them(graph) else where. This can be as a map from vertices to their adjacency lists as shown below :-

#include<bits/stdc++.h>
using namespace std;

/* implement the graph as a map from the integer index as a key to the   adjacency list
 * of the graph implemented as a vector being the value of each individual key. The
 * program will be given a matrix of numbers, the first element of each row will
 * represent the head of the adjacency list and the rest of the elements will be the
 * list of that element in the graph.
*/

typedef map<int, vector<int> > graphType;

int main(){

graphType graph;
int vertices = 0;

cout << "Please enter the number of vertices in the graph :- " << endl;
cin >> vertices;
if(vertices <= 0){
    cout << "The number of vertices in the graph can't be less than or equal to 0." << endl;
    exit(0);
}

cout << "Please enter the elements of the graph, as an adjacency list, one row after another. " << endl;
for(int i = 0; i <= vertices; i++){

    vector<int> adjList;                    //the vector corresponding to the adjacency list of each vertex

    int key = -1, listValue = -1;
    string listString;
    getline(cin, listString);
    if(i != 0){
        istringstream iss(listString);
        iss >> key;
        iss >> listValue;
        if(listValue != -1){
            adjList.push_back(listValue);
            for(; iss >> listValue; ){
                adjList.push_back(listValue);
            }
            graph.insert(graphType::value_type(key, adjList));
        }
        else
            graph.insert(graphType::value_type(key, adjList));
    }
}

//print the elements of the graph
cout << "The graph that you entered :- " << endl;
for(graphType::const_iterator iterator = graph.begin(); iterator != graph.end(); ++iterator){
    cout << "Key : " << iterator->first << ", values : ";

    vector<int>::const_iterator vectBegIter = iterator->second.begin();
    vector<int>::const_iterator vectEndIter = iterator->second.end();
    for(; vectBegIter != vectEndIter; ++vectBegIter){
        cout << *(vectBegIter) << ", ";
    }
    cout << endl;
}
}

Answer 6

Below is a implementation of Graph Data Structure in C++ as Adjacency List.

I have used STL vector for representation of vertices and STL pair for denoting edge and destination vertex.

#include <iostream>
#include <vector>
#include <map>
#include <string>

using namespace std;

struct vertex {
    typedef pair<int, vertex*> ve;
    vector<ve> adj; //cost of edge, destination vertex
    string name;
    vertex(string s) : name(s) {}
};

class graph
{
public:
    typedef map<string, vertex *> vmap;
    vmap work;
    void addvertex(const string&);
    void addedge(const string& from, const string& to, double cost);
};

void graph::addvertex(const string &name)
{
    vmap::iterator itr = work.find(name);
    if (itr == work.end())
    {
        vertex *v;
        v = new vertex(name);
        work[name] = v;
        return;
    }
    cout << "\nVertex already exists!";
}

void graph::addedge(const string& from, const string& to, double cost)
{
    vertex *f = (work.find(from)->second);
    vertex *t = (work.find(to)->second);
    pair<int, vertex *> edge = make_pair(cost, t);
    f->adj.push_back(edge);
}