note: 連通是無向圖中的概念

接下來介紹兩個演算法：判斷圖的連通性與標記連通分量。

1. 判斷一個圖是否連通. Determine whether an undirected graph is connected

class Undirected : virtual public Network {
 public:
  bool Connected();
};

bool Undirected::Connect()
{// Return true iff graph is connected.
 
 int n = Vertices();
 
 // set all vertices as not reached
 int *reach = new int [n+1];
 for (int i = 1; i <= n; i++)
  reach[i] = 0;

 //mark vertices reachable from vertex 1
 DFS(1, reach, 1);

 //check if all vertices marked
 for (int i = 1; i<= n; i++)
  if (!reach[i]) return false;
 return true;
}
 

下面這個程式的複雜性是O(n^2); 用鄰接連結串列描述圖時，是O(n+e)

int Undirected::LabelComponents(int L[])
{// Label the components of the graph.
 //Return the number of components and set L[1:n] to represent a labeling of vertices by component.

 int n = Vertices();

 // assign all vertices to no component
 for (int i = 1; i<=n; i++)
  L[i] = 0;
 
 int label = 0; // ID of last component
 // identify components
 for (int i = 1; i <= n; i++)
 { 
  if(!L[i]){// unreached vertex
   //vertex i is in a new component
   label++;
   BFS(i, L, label);
  }// mark new component
 }
 return label;
}