C++ Set Comparator Data Structure - c++

Question

I am using a C++ STL set with a custom comparator to store an Edge data structure as shown below. I defined the Edge to be essentially a key-value pair. Index is the key and I want to iterate through the collection by value (maxlength) from largest to smallest. At any given time, I usually only care about the edges with the 3 largest values. There will only be a relatively small number of edges in the collection ranging from around 7 to 64. When I insert an edge, the values of the two adjacent edges will need to be adjusted. To do this, I will add the new edge to the set, then remove the two adjacent edges and re-add them with their new values. Can anyone share a more efficient data structure for this purpose?
#include <iostream>
#include <iomanip>
#include <sstream>
#include <set>
using namespace std;
struct Edge {
int maxlength;
int index;
Edge(int index, int maxlength) {
this->maxlength = maxlength;
this->index = index;
}
bool operator<(Edge other) const {
return maxlength < other.maxlength;
}
};
void run() {
set<Edge> edges;
edges.insert(Edge(25, 3));
edges.insert(Edge(21, 4));
edges.insert(Edge(28, 2));
cout << "First Edge: " << edges.begin()->maxlength << endl;
edges.erase(Edge(28, 2));
cout << "First Edge: " << edges.begin()->maxlength << endl;
edges.insert(Edge(39, 1));
cout << "First Edge: " << edges.begin()->maxlength << endl;
cout << "Last Edge: " << (--edges.end())->maxlength << endl;
}
int main() {
run();
return 1;
}