查找无向图的所有派系 [英] Finding All Cliques of an Undirected Graph
本文介绍了查找无向图的所有派系的处理方法,对大家解决问题具有一定的参考价值,需要的朋友们下面随着小编来一起学习吧!
问题描述
如何列出无向图的所有派系? (并非所有最大派系都像Bron-Kerbosch算法一样)
How can I list all cliques of an Undirected Graph ? (Not all maximal cliques, like the Bron-Kerbosch algorithm)
推荐答案
最优解决方案是这样的,因为在一个完整的图中有2 ^ n个团.考虑使用递归函数的所有节点子集.对于每个子集,如果子集的节点之间都存在所有边,则将1加到您的计数器中:(这几乎是C ++中的伪代码)
The optimal solution is like this because in a complete graph there are 2^n cliques. Consider all subsets of nodes using a recursive function. And for each subset if all the edges are present between nodes of the subset, add 1 to your counter: (This is almost a pseudocode in C++)
int clique_counter = 0;
int n; //number of nodes in graph
//i imagine nodes are numbered from 1 to n
void f(int x, vector <int> &v){ //x is the current node
if(x == n){
bool is_clique = true;
for(int i = 0; i < v.size(); i++){
for(int j = i + 1; j < v.size(); j++){
if(there is not an edge between node v[i] and v[j]) //it can't be clique
is_clique = false;
}
}
if(is_clique == true){
clique_counter++;
}
return;
}
//if x < n
f(x + 1, v);
v.push_back(x);
f(x + 1, v);
v.pop_back();
}
int main(){
vector <int> v;
f(1, v);
cout << clique_counter << endl;
return 0;
}
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